Coefficient of Friction Between Body and Wedge

NEET > Physics > Laws of Motion > Friction > Coefficient of Friction Between Body and Wedge

Unit Progress

NEET Physics — Friction

Coefficient of Friction Between Body and Wedge – Complete Notes, Revision, Important Questions & Downloads

Coefficient of Friction Between Body and Wedge covers the TOC subtopic Wedge Friction Formula. A body slides on a smooth wedge of angle θ in time t. On the rough version of the same wedge, it takes nt (n > 1 times longer). From these two conditions, the coefficient of friction is μ = tanθ[1 − 1/n²]. NEET tests this as a direct substitution problem: given θ, t, nt, find μ. The key steps are setting equal distances from both smooth and rough cases and solving for μ.

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Wedge Friction FormulaFriction Ch.5Same Distance, Different Times

Expected QuestionsQ

0–1

NEET asks: given wedge angle θ and time ratio n, find μ = tanθ(1−1/n²). Or the inverse: given μ and θ, find n. Occasionally asks to compare accelerations on smooth vs rough wedge. The formula is derived by equating the distance travelled in time t (smooth) with distance in time nt (rough): same incline length S = ½ a₁ t² = ½ a₂ (nt)².

Time Required⏱

20 min

10 min to derive: write a₁ = gsinθ (smooth), a₂ = g(sinθ − μcosθ) (rough). S = ½a₁t² = ½a₂(nt)². Divide: a₁/a₂ = n². Substitute and solve for μ. 10 min to practise with numbers: e.g., θ=30°, n=2 → μ = tan30°(1−1/4) = (1/√3)(3/4) = 3/(4√3) = √3/4.

Difficulty⚡

Medium

The derivation requires recognising that both cases study the same distance (the length of the wedge): S is the same, only the time differs. Setting up S = ½ a₁ t² and S = ½ a₂ (nt)², then dividing to get a₁/a₂ = n² is the key algebraic step. Once that ratio is established, substituting a₁ = gsinθ and a₂ = g(sinθ − μcosθ) gives μ directly.

NRI USA Curriculum GapUS

Medium

AP Physics 1 covers kinematics on inclines and friction, but not the 'compare smooth vs rough descent time' problem as a named result. The formula μ = tanθ(1−1/n²) is NEET-specific. NRI students comfortable with kinematics can derive it, but must know to equate same-distance conditions.

1Subtopics

4+Practice Questions

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20 minPrep Time

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NEET Weightage — Coefficient of Friction Between Body and Wedge

Friction (Chapter 5)

NEET Year	Questions from this Topic	Bar	Marks
2024	0	0 Q	0
2023	1	1 Q	4
2022	0	0 Q	0
2021	1	1 Q	4
2020	0	0 Q	0
2019	0	0 Q	0
6-Year Total (2019–2024)	0–2		0–8

SETUP: A wedge of angle θ has length S along the incline. Case 1 (smooth): a₁ = gsinθ. Body starts from rest, reaches bottom in time t. S = ½ gsinθ · t². Case 2 (rough, same wedge): a₂ = g(sinθ − μcosθ). Body starts from rest, takes time nt. S = ½ g(sinθ − μcosθ) · (nt)².
DERIVATION: Equate S: ½ gsinθ · t² = ½ g(sinθ − μcosθ) · n²t² → gsinθ = n²g(sinθ − μcosθ) → sinθ = n²sinθ − n²μcosθ → n²μcosθ = n²sinθ − sinθ = sinθ(n²−1) → μ = sinθ(n²−1)/(n²cosθ) = tanθ(1 − 1/n²).
RESULT: μ = tanθ[1 − 1/n²]. Special cases: n=1 (same time = smooth wedge): μ = 0 ✓. n→∞ (body barely moves on rough wedge): μ → tanθ (coefficient equals tangent of angle — body on verge of not sliding). For n=2 and θ=30°: μ = tan30°(1−1/4) = (1/√3)(3/4) = 3/(4√3) = √3/4 ≈ 0.433.

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Avg Questions / Year

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Total Marks (6 yrs)

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Direct

Pattern

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Medium

Difficulty

How to Solve the Wedge Friction Coefficient Problem

Step 1 — Write accelerations for both cases Smooth: a₁ = gsinθ. Rough: a₂ = g(sinθ − μcosθ). Both motions start from rest along the same incline length S.

Step 2 — Equate distances S = ½a₁t² and S = ½a₂(nt)². Therefore a₁t² = a₂n²t² → a₁ = n²a₂ → ratio a₁/a₂ = n².

Step 3 — Solve for μ gsinθ = n²g(sinθ − μcosθ) → sinθ = n²sinθ − n²μcosθ → n²μcosθ = sinθ(n²−1) → μ = tanθ(n²−1)/n² = tanθ[1−1/n²].

Study Materials — Coefficient of Friction Between Body and Wedge

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Full Notes

Smooth: a₁=gsinθ, time=t. Rough: a₂=g(sinθ−μcosθ), time=nt. Same S: a₁t²=a₂(nt)² → gsinθ=n²g(sinθ−μcosθ) → μ=tanθ(1−1/n²). Limiting case: n→∞ → μ→tanθ (angle of repose).

1 subtopicKinematics + frictionDirect formula

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Formula Sheet

a₁=gsinθ; a₂=g(sinθ−μcosθ); a₁/a₂=n²; μ=tanθ(1−1/n²). Inverse: given μ,θ → n=1/√(1−μ/tanθ).

4 formulas1 pageQuick reference

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MCQ Practice

8 MCQs on wedge friction formula, time ratios, and inverse problems — find n from μ and θ.

8 MCQs1 formulaSolved

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PYQ

Previous year NEET questions on wedge friction with complete solutions and time-ratio analysis.

2+ year-tagged Qs2015–2024Solved

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Subtopics — Coefficient of Friction Between Body and Wedge

2-Column Table

Column A	Column B
Wedge Friction Formula↗

Rapid Revision — Coefficient of Friction Between Body and Wedge

Concept → Trap → Example

1) Wedge Friction Formula — Deriving μ = tanθ(1−1/n²)

Wedge Friction Formula

PROBLEM: A body slides from rest on a frictionless wedge (angle θ) in time t, reaching the bottom. On the same wedge with friction (coefficient μ), starting from rest, the body takes n times longer (time = nt). Derive μ in terms of θ and n. SMOOTH CASE: Acceleration a₁ = gsinθ. Distance S = ½a₁t². ROUGH CASE: Forces along incline: gravity component down = mgsinθ; friction (resisting motion, up the incline) = μN = μmgcosθ. Net force = mg(sinθ − μcosθ). Acceleration a₂ = g(sinθ − μcosθ). Same distance S = ½a₂(nt)² (starts from rest, takes time nt). EQUATING S: ½a₁t² = ½a₂(nt)² → a₁ = n²a₂ → gsinθ = n²g(sinθ − μcosθ) → sinθ = n²sinθ − n²μcosθ → n²μcosθ = n²sinθ − sinθ = sinθ(n²−1) → μ = [sinθ(n²−1)]/(n²cosθ) = tanθ × (n²−1)/n² = tanθ[1 − 1/n²]. RESULT: μ = tanθ(1 − 1/n²). Alternatively: μ = tanθ(n²−1)/n².

PHYSICAL INTERPRETATION: For n=1 (rough wedge takes same time as smooth): μ = tanθ(1−1) = 0 — consistent, no friction. For n→∞ (body barely slides on rough wedge): μ → tanθ — the coefficient approaches tanθ, which is exactly the angle-of-repose condition (body on the verge of not sliding). So the formula captures both extremes correctly.
INVERSE PROBLEM: Given μ and θ, find n. From μ = tanθ(1−1/n²): μ/tanθ = 1−1/n² → 1/n² = 1 − μ/tanθ → n² = 1/(1 − μ/tanθ) = tanθ/(tanθ − μ) → n = √[tanθ/(tanθ − μ)]. This is the time ratio. Condition for body to slide: μ < tanθ (otherwise body doesn't slide at all on rough wedge, n→∞).
NEET TRAP: Students mix up which wedge is smooth and which is rough, or forget the n² factor from squaring the time ratio. The key algebraic step is: same distance S means a₁t² = a₂(nt)² → a₁ = n²a₂. Write this ratio immediately after stating both accelerations. The n² comes from squaring the time ratio (not from linear ratio).

Example (NEET-style)Wedge angle θ=45°, body takes 2 seconds on smooth wedge and 4 seconds on rough wedge. n = 4/2 = 2. μ = tan45°(1−1/4) = 1×(3/4) = 0.75. If θ=30° and n=2: μ = tan30°×(3/4) = (1/√3)×(3/4) = 3/(4√3) = (3√3)/12 = √3/4 ≈ 0.433.

US Curriculum Gaps — Coefficient of Friction Between Body and Wedge

Topics in this section are in NEET but may be framed differently in US physics courses.

Kinematic Time Comparison on Inclines in AP Physics 1

AP Physics 1 covers friction on inclined planes but does not test the specific comparison between smooth and rough descent times as a method to compute friction coefficient. The formula μ = tanθ(1−1/n²) does not appear in AP Physics curriculum. NRI students with strong kinematics can derive it but need to recognise the 'equate distances' approach.

AP Physics 1: friction on inclines covered; time-ratio method to find μ not tested
NEET: μ = tanθ(1−1/n²) is a direct-formula question — memorise and apply in under 30 seconds
Key step: a₁t² = a₂(nt)² → a₁/a₂ = n² — the n² ratio from squaring time is the critical algebraic manipulation

Angle of Repose Connection in University Physics

Halliday & Resnick introduces angle of repose (tanθ = μ) as the incline angle at which an object just begins to slide. The wedge formula μ = tanθ(1−1/n²) shows that the limiting case (n→∞) recovers the angle-of-repose condition. This connection between dynamic and static friction on inclines is typically not made explicit in US university courses at the level of NEET problems.

US university: angle of repose defined but smooth/rough time comparison not a standard problem type
NEET: the formula μ=tanθ(1−1/n²) directly connects to angle-of-repose when n→∞
Memorisation: write μ = tanθ(1−1/n²); verify units — μ is dimensionless, tanθ is dimensionless ✓

NEET-Style Practice — Coefficient of Friction Between Body and Wedge

4 Questions

1A body slides from rest on a smooth inclined plane of angle 30° and reaches the bottom in 2 seconds. On the same rough inclined plane it takes 4 seconds. The coefficient of friction is:Wedge Friction Formula

0.433

0.577

0.250

0.750

n = 4/2 = 2. μ = tan30°(1−1/n²) = (1/√3)(1−1/4) = (1/√3)(3/4) = 3/(4√3) = (3/4)×(1/√3) = (3)/(4√3) = √3/4 ≈ 1.732/4 ≈ 0.433. Answer: Option A. Verify: a₁=gsin30°=5 m/s²; S=½×5×4=10 m. a₂=g(sin30°−0.433cos30°)=10(0.5−0.433×0.866)=10(0.5−0.375)=10×0.125=1.25 m/s². S=½×1.25×16=10 m ✓.

2On a smooth inclined plane (angle 45°), a body descends in time t. On the rough version of the same incline, it descends in time √2·t. The coefficient of friction between body and incline is:Finding μ with n=√2

0.25

0.50

0.75

1.00

n = √2. n² = 2. μ = tan45°(1−1/2) = 1×(1/2) = 0.5. Answer: Option B. Verify: a₁=gsin45°=g/√2; a₂=g(sin45°−0.5cos45°)=g(1/√2−0.5/√2)=g×0.5/√2=g/(2√2)=a₁/2. Same distance: a₁t²=a₂(√2t)² → a₁t²=(a₁/2)×2t²=a₁t² ✓.

3On a rough inclined plane of angle θ (with μ = tanθ/4), a body starts from rest. Compared to the same body on a smooth incline of same angle, the time ratio (rough/smooth) is:Finding n from μ

n = 2/√3

n = √2

n = 2

n = 4/3

From μ = tanθ(1−1/n²): tanθ/4 = tanθ(1−1/n²) → 1/4 = 1−1/n² → 1/n² = 1−1/4 = 3/4 → n² = 4/3 → n = 2/√3. Answer: Option A. Check: n=2/√3, n²=4/3. μ=tanθ(1−3/4)=tanθ/4 ✓.

4A body slides on a smooth wedge of angle θ and its time of descent is t. If the same wedge is made rough, the body takes 2t to descend. The frictional force as a fraction of weight of body is:Friction Force Fraction

3sinθ/4

3cosθ/4

sinθ/4

μcosθ (cannot simplify)

n = 2. μ = tanθ(1−1/4) = (3/4)tanθ = (3sinθ)/(4cosθ). Friction force = μmgcosθ = [(3sinθ)/(4cosθ)]×mgcosθ = (3mgsinθ)/4. As fraction of weight mg: f/mg = 3sinθ/4. Option A is correct. Note: this means friction = (3/4) of the gravity component along the incline (mgsinθ). The total retarding effect is mgsinθ + friction (up the slope) on smooth = mgsinθ only; on rough = mgsinθ + (3mgsinθ/4) ... wait, friction acts UP the slope (opposes motion down), so a₂ = g(sinθ − μcosθ) = g(sinθ − 3sinθ/4) = gsinθ/4. Check: a₁=gsinθ, a₂=gsinθ/4, ratio=4=n²=4 ✓.

Practice Problems — Coefficient of Friction Between Body and Wedge

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1A body slides down a smooth wedge (angle 60°) in 1 second. The same body takes 3 seconds on the same rough wedge. Find μ.

μ = tan60°(1−1/9) = √3×(8/9) = 8√3/9 ≈ 1.54 — which exceeds physically reasonable values; verify setup

μ = tan60°(1−1/9) = 8√3/9 ≈ 1.54 (valid if surface is extremely rough)

μ = 1/√3

μ = 0.5

👁 Reveal Answer

n=3, n²=9. μ=tan60°(1−1/9)=√3×(8/9)=8√3/9≈1.54. This is a physically large μ (rough rubber on granite can approach 1–1.8), so it's possible. Verification: a₁=g×(√3/2)≈8.66 m/s²(if θ=60°, a₁=gsin60°=10×0.866=8.66 m/s²). a₂=g(sin60°−μcos60°)=10(0.866−1.54×0.5)=10(0.866−0.77)=10×0.096=0.96 m/s². Ratio a₁/a₂=8.66/0.96=9.02≈9=n² ✓.

2For a wedge of angle θ and time ratio n, what is the condition on μ for the body to actually slide on the rough wedge?

μ < sinθ

μ < tanθ (coefficient must be less than the tangent of the wedge angle)

μ > cosθ

μ < cosθ

👁 Reveal Answer

For sliding, the net force along the incline must be positive: g(sinθ−μcosθ) > 0 → sinθ > μcosθ → μ < sinθ/cosθ = tanθ. So μ < tanθ is the condition. If μ ≥ tanθ, the body stays at rest (friction is large enough to prevent motion). In the formula μ = tanθ(1−1/n²): for real n>1, (1−1/n²) is between 0 and 1, so μ is always strictly less than tanθ ✓ — the formula automatically satisfies the sliding condition for n > 1. Answer: Option B.

3On a smooth incline (angle 30°) a block slides in 2s. On a rough identical incline it slides in time T. If μ = 0.2, find T.

T = 2√2 s ≈ 2.83 s

T = 4 s

T = 2√(sin30°/(sin30°−0.2cos30°)) s

T = 2√(10/6.27) ≈ 3.56 s

👁 Reveal Answer

n = T/2. From μ = tanθ(1−1/n²): 0.2 = tan30°(1−1/n²) = (1/√3)(1−1/n²) → 1−1/n² = 0.2√3 = 0.3464 → 1/n² = 1−0.3464 = 0.6536 → n² = 1.530 → n = 1.237. T = 2n = 2×1.237 = 2.47 s. Alternative: a₂=g(sin30°−0.2cos30°)=10(0.5−0.2×0.866)=10(0.5−0.1732)=10×0.3268=3.268 m/s². S=½×gsin30°×4=½×5×4=10 m. T²=2S/a₂=20/3.268=6.12 → T=2.47 s ✓. Answer: close to Option D but exact value is 2.47 s.

4A body slides down a smooth wedge angle θ in time t and the rough wedge of same angle in time nt. Write the expression for the acceleration on the rough wedge in terms of gsinθ and n.

a₂ = gsinθ/n

a₂ = gsinθ/n²

a₂ = gsinθ(1−1/n)

a₂ = gsinθ × n²

👁 Reveal Answer

From same-distance condition: a₁t² = a₂(nt)² → a₁ = n²a₂ → a₂ = a₁/n² = gsinθ/n². Answer: Option B. This directly gives the acceleration on the rough incline. Then: a₂ = g(sinθ−μcosθ) = gsinθ/n² → gsinθ − μgcosθ = gsinθ/n² → μgcosθ = gsinθ(1−1/n²) → μ = tanθ(1−1/n²). The result a₂ = gsinθ/n² is the intermediate formula from which μ is extracted.

Physics — Friction Revision Checklist

Check off chapters as you revise

Use this section for quick chapter tracking before mocks, part tests, and final NEET revision.

Wedge Friction Formula: Write μ = tanθ(1−1/n²) from memory and state what n represents (time ratio: rough time / smooth time).

Wedge Friction Formula: Derive the formula from scratch: a₁=gsinθ, a₂=g(sinθ−μcosθ), same S → a₁t²=a₂(nt)² → a₁=n²a₂ → solve for μ.

Wedge Friction Formula: Verify the limiting cases: n=1 → μ=0 (no friction); n→∞ → μ=tanθ (angle of repose). These boundary checks validate the formula.

Wedge Friction Formula: Solve the inverse: given μ and θ, find n = √[tanθ/(tanθ−μ)]. Verify n>1 (rough takes longer than smooth) and μ<tanθ (sliding condition).

Wedge Friction Formula: Practise: θ=45°, n=2 → μ=1×(3/4)=0.75. θ=30°, n=√2 → μ=tan30°×(1−1/2)=1/(2√3)≈0.289. θ=60°, n=2 → μ=√3×(3/4)=3√3/4≈1.3.

FAQ — Coefficient of Friction Between Body and Wedge

Notes · Downloads · Revision · Important Questions

What is the formula for coefficient of friction on a wedge when time ratio is n?

μ = tanθ[1 − 1/n²], where θ is the wedge angle and n is the ratio (time on rough wedge) / (time on smooth wedge). The body starts from rest in both cases and travels the same distance along the wedge.

Why does the formula use n² and not n?

Because distance ∝ t² (kinematics from rest: S = ½at²). The condition 'same distance' gives a₁t² = a₂(nt)², so a₁/a₂ = n² — the acceleration ratio equals the square of the time ratio (not the linear time ratio). This is the source of n² in the formula, not n.

What does the formula predict for n = 1?

When n=1, the rough wedge takes the same time as the smooth wedge, meaning friction has no effect. Substituting: μ = tanθ(1−1) = 0. This is consistent — if μ=0, the wedge is smooth, so n=1 ✓.

What does n → ∞ mean physically?

n → ∞ means the body takes infinitely long to slide down the rough wedge — it is barely moving, on the verge of not sliding at all. In this limit μ → tanθ, which is the angle-of-repose condition (maximum μ for sliding to occur on an incline of angle θ). So the formula is consistent with the angle-of-repose result in the limiting case.

What is the condition for the body to slide on the rough wedge at all?

μ < tanθ. If μ ≥ tanθ, friction is large enough to prevent sliding entirely (static friction balances the gravitational component). The formula μ = tanθ(1−1/n²) automatically satisfies this condition for any finite n > 1, since (1−1/n²) < 1 for all finite n.

Can I apply this formula if the body is being pushed up the rough wedge instead of sliding down?

No. The formula μ = tanθ(1−1/n²) was derived for sliding down (friction acts up along the incline, opposing motion). For a body being pushed up, friction acts down the incline (opposing upward motion), and the net deceleration would be a = g(sinθ + μcosθ). A different comparison would yield a different formula for μ.

If the body descends in 2s (smooth) and 4s (rough), does the rough wedge have exactly 4× greater resistance?

No — the rough wedge has greater resistance compared to smooth, but not 4×. n=2, n²=4. The acceleration ratio a₁/a₂ = 4 means the smooth acceleration is 4 times the rough acceleration. But friction force = μmgcosθ and gravity component = mgsinθ; the net on rough wedge = mg(sinθ−μcosθ) = mgsinθ/4. The ratio 4 applies to accelerations, not to forces compared to friction alone.

What if I know μ and want to find the time ratio n?

From μ = tanθ(1−1/n²): μ/tanθ = 1−1/n² → 1/n² = 1 − μ/tanθ → n² = tanθ/(tanθ−μ) → n = √[tanθ/(tanθ−μ)]. Condition: μ < tanθ (body must be able to slide). Example: θ=45°, μ=0.5: n=√[1/(1−0.5)]=√2 ≈ 1.41.

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Coefficient of Friction Between Body and Wedge

NEET > Physics > Laws of Motion > Friction > Coefficient of Friction Between Body and Wedge

Unit Progress

NEET Physics — Friction

Coefficient of Friction Between Body and Wedge – Complete Notes, Revision, Important Questions & Downloads

⬇ Download Notes PDF View Important Questions →

Wedge Friction FormulaFriction Ch.5Same Distance, Different Times

Expected QuestionsQ

0–1

Time Required⏱

20 min

Difficulty⚡

Medium

NRI USA Curriculum GapUS

Medium

1Subtopics

4+Practice Questions

4Free Downloads

20 minPrep Time

⬇ Get Free Downloads

NEET Weightage — Coefficient of Friction Between Body and Wedge

Friction (Chapter 5)

NEET Year	Questions from this Topic	Bar	Marks
2024	0	0 Q	0
2023	1	1 Q	4
2022	0	0 Q	0
2021	1	1 Q	4
2020	0	0 Q	0
2019	0	0 Q	0
6-Year Total (2019–2024)	0–2		0–8

📊

0.3

Avg Questions / Year

🎯

Total Marks (6 yrs)

📈

Direct

Pattern

⚠️

Medium

Difficulty

How to Solve the Wedge Friction Coefficient Problem

Step 1 — Write accelerations for both cases Smooth: a₁ = gsinθ. Rough: a₂ = g(sinθ − μcosθ). Both motions start from rest along the same incline length S.

Step 2 — Equate distances S = ½a₁t² and S = ½a₂(nt)². Therefore a₁t² = a₂n²t² → a₁ = n²a₂ → ratio a₁/a₂ = n².

Step 3 — Solve for μ gsinθ = n²g(sinθ − μcosθ) → sinθ = n²sinθ − n²μcosθ → n²μcosθ = sinθ(n²−1) → μ = tanθ(n²−1)/n² = tanθ[1−1/n²].

Study Materials — Coefficient of Friction Between Body and Wedge

PDF · Cheat Sheet · MCQ Set · PYQ

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Full Notes

1 subtopicKinematics + frictionDirect formula

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📗

Formula Sheet

a₁=gsinθ; a₂=g(sinθ−μcosθ); a₁/a₂=n²; μ=tanθ(1−1/n²). Inverse: given μ,θ → n=1/√(1−μ/tanθ).

4 formulas1 pageQuick reference

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MCQ Practice

8 MCQs on wedge friction formula, time ratios, and inverse problems — find n from μ and θ.

8 MCQs1 formulaSolved

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PYQ

Previous year NEET questions on wedge friction with complete solutions and time-ratio analysis.

2+ year-tagged Qs2015–2024Solved

Download PYQs

Subtopics — Coefficient of Friction Between Body and Wedge

2-Column Table

Column A	Column B
Wedge Friction Formula↗

Rapid Revision — Coefficient of Friction Between Body and Wedge

Concept → Trap → Example

1) Wedge Friction Formula — Deriving μ = tanθ(1−1/n²)

Wedge Friction Formula

PHYSICAL INTERPRETATION: For n=1 (rough wedge takes same time as smooth): μ = tanθ(1−1) = 0 — consistent, no friction. For n→∞ (body barely slides on rough wedge): μ → tanθ — the coefficient approaches tanθ, which is exactly the angle-of-repose condition (body on the verge of not sliding). So the formula captures both extremes correctly.
INVERSE PROBLEM: Given μ and θ, find n. From μ = tanθ(1−1/n²): μ/tanθ = 1−1/n² → 1/n² = 1 − μ/tanθ → n² = 1/(1 − μ/tanθ) = tanθ/(tanθ − μ) → n = √[tanθ/(tanθ − μ)]. This is the time ratio. Condition for body to slide: μ < tanθ (otherwise body doesn't slide at all on rough wedge, n→∞).
NEET TRAP: Students mix up which wedge is smooth and which is rough, or forget the n² factor from squaring the time ratio. The key algebraic step is: same distance S means a₁t² = a₂(nt)² → a₁ = n²a₂. Write this ratio immediately after stating both accelerations. The n² comes from squaring the time ratio (not from linear ratio).

US Curriculum Gaps — Coefficient of Friction Between Body and Wedge

Topics in this section are in NEET but may be framed differently in US physics courses.

Kinematic Time Comparison on Inclines in AP Physics 1

AP Physics 1: friction on inclines covered; time-ratio method to find μ not tested
NEET: μ = tanθ(1−1/n²) is a direct-formula question — memorise and apply in under 30 seconds
Key step: a₁t² = a₂(nt)² → a₁/a₂ = n² — the n² ratio from squaring time is the critical algebraic manipulation

Angle of Repose Connection in University Physics

US university: angle of repose defined but smooth/rough time comparison not a standard problem type
NEET: the formula μ=tanθ(1−1/n²) directly connects to angle-of-repose when n→∞
Memorisation: write μ = tanθ(1−1/n²); verify units — μ is dimensionless, tanθ is dimensionless ✓

NEET-Style Practice — Coefficient of Friction Between Body and Wedge

4 Questions

0.433

0.577

0.250

0.750

0.25

0.50

0.75

1.00

3On a rough inclined plane of angle θ (with μ = tanθ/4), a body starts from rest. Compared to the same body on a smooth incline of same angle, the time ratio (rough/smooth) is:Finding n from μ

n = 2/√3

n = √2

n = 2

n = 4/3

3sinθ/4

3cosθ/4

sinθ/4

μcosθ (cannot simplify)

Practice Problems — Coefficient of Friction Between Body and Wedge

Click "Reveal Answer" after attempting

1A body slides down a smooth wedge (angle 60°) in 1 second. The same body takes 3 seconds on the same rough wedge. Find μ.

μ = tan60°(1−1/9) = √3×(8/9) = 8√3/9 ≈ 1.54 — which exceeds physically reasonable values; verify setup

μ = tan60°(1−1/9) = 8√3/9 ≈ 1.54 (valid if surface is extremely rough)

μ = 1/√3

μ = 0.5

👁 Reveal Answer

2For a wedge of angle θ and time ratio n, what is the condition on μ for the body to actually slide on the rough wedge?

μ < sinθ

μ < tanθ (coefficient must be less than the tangent of the wedge angle)

μ > cosθ

μ < cosθ

👁 Reveal Answer

3On a smooth incline (angle 30°) a block slides in 2s. On a rough identical incline it slides in time T. If μ = 0.2, find T.

T = 2√2 s ≈ 2.83 s

T = 4 s

T = 2√(sin30°/(sin30°−0.2cos30°)) s

T = 2√(10/6.27) ≈ 3.56 s

👁 Reveal Answer

4A body slides down a smooth wedge angle θ in time t and the rough wedge of same angle in time nt. Write the expression for the acceleration on the rough wedge in terms of gsinθ and n.

a₂ = gsinθ/n

a₂ = gsinθ/n²

a₂ = gsinθ(1−1/n)

a₂ = gsinθ × n²

👁 Reveal Answer

Physics — Friction Revision Checklist

Check off chapters as you revise

Use this section for quick chapter tracking before mocks, part tests, and final NEET revision.

Wedge Friction Formula: Write μ = tanθ(1−1/n²) from memory and state what n represents (time ratio: rough time / smooth time).

Wedge Friction Formula: Derive the formula from scratch: a₁=gsinθ, a₂=g(sinθ−μcosθ), same S → a₁t²=a₂(nt)² → a₁=n²a₂ → solve for μ.

Wedge Friction Formula: Verify the limiting cases: n=1 → μ=0 (no friction); n→∞ → μ=tanθ (angle of repose). These boundary checks validate the formula.

Wedge Friction Formula: Solve the inverse: given μ and θ, find n = √[tanθ/(tanθ−μ)]. Verify n>1 (rough takes longer than smooth) and μ<tanθ (sliding condition).

Wedge Friction Formula: Practise: θ=45°, n=2 → μ=1×(3/4)=0.75. θ=30°, n=√2 → μ=tan30°×(1−1/2)=1/(2√3)≈0.289. θ=60°, n=2 → μ=√3×(3/4)=3√3/4≈1.3.

FAQ — Coefficient of Friction Between Body and Wedge

Notes · Downloads · Revision · Important Questions

What is the formula for coefficient of friction on a wedge when time ratio is n?

Why does the formula use n² and not n?

What does the formula predict for n = 1?

What does n → ∞ mean physically?

What is the condition for the body to slide on the rough wedge at all?

Can I apply this formula if the body is being pushed up the rough wedge instead of sliding down?

If the body descends in 2s (smooth) and 4s (rough), does the rough wedge have exactly 4× greater resistance?

What if I know μ and want to find the time ratio n?

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Wedge Friction Formula

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Wedge Friction Formula

Newton's Laws of Motion

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Friction

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Coefficient of Friction Between Body and Wedge

Coefficient of Friction Between Body and Wedge – Complete Notes, Revision, Important Questions & Downloads

1) Wedge Friction Formula — Deriving μ = tanθ(1−1/n²)

Kinematic Time Comparison on Inclines in AP Physics 1

Angle of Repose Connection in University Physics

Physics — Friction Revision Checklist

NEET NRI Counseling & Admission eBook Download

Schedule Trial Session For NEET Prep

Wedge Friction Formula

Subtopics

Wedge Friction Formula

NEET > Physics > Laws of Motion Chapters

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Coefficient of Friction Between Body and Wedge

Coefficient of Friction Between Body and Wedge – Complete Notes, Revision, Important Questions & Downloads

1) Wedge Friction Formula — Deriving μ = tanθ(1−1/n²)

Kinematic Time Comparison on Inclines in AP Physics 1

Angle of Repose Connection in University Physics

Physics — Friction Revision Checklist

NEET NRI Counseling & Admission eBook Download

Schedule Trial Session For NEET Prep

Wedge Friction Formula

Subtopics

Wedge Friction Formula

NEET > Physics > Laws of Motion Chapters

Comments

Leave a comment

Comments (0)

Coefficient of Friction Between Body and Wedge

Overview content

Coefficient of Friction Between Body and Wedge – Complete Notes, Revision, Important Questions & Downloads

1) Wedge Friction Formula — Deriving μ = tanθ(1−1/n²)

Kinematic Time Comparison on Inclines in AP Physics 1

Angle of Repose Connection in University Physics

Physics — Friction Revision Checklist

NEET NRI Counseling & Admission eBook Download

Schedule Trial Session For NEET Prep

Wedge Friction Formula

Subtopics

Wedge Friction Formula

NEET > Physics > Laws of Motion Chapters

Comments

Leave a comment

Comments (0)

Coefficient of Friction Between Body and Wedge

Overview content

Coefficient of Friction Between Body and Wedge – Complete Notes, Revision, Important Questions & Downloads

1) Wedge Friction Formula — Deriving μ = tanθ(1−1/n²)

Kinematic Time Comparison on Inclines in AP Physics 1

Angle of Repose Connection in University Physics

Physics — Friction Revision Checklist

NEET NRI Counseling & Admission eBook Download

Schedule Trial Session For NEET Prep

Wedge Friction Formula

Subtopics

Wedge Friction Formula

NEET > Physics > Laws of Motion Chapters

Comments

Leave a comment

Comments (0)