A cylinder, hollow sphere, solid sphere and a ring all having mass 1 kg are released from rest on a…

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A cylinder, hollow sphere, solid sphere and a ring all having mass 1 kg are released from rest on a inclined plane having angle of inclination 37° (tan 37° = 3/4). Coefficient of friction between bodies and plane is 'µ', then match the following column .
Column IColumn II(i) If µ < 0.25 body which must not undergo pure rolling motion[A] Ring(ii) If µ  0.3 work done by friction must be negative for[B] Hollow sphere(iii) If µ = 0.4, total mechanical energy will be conserved for[C] Solid sphere(iv) If µ = 0.25, friction force will be 2N for[D] Cylinder

CGP Edu Experts · Accepted Answer

The correct answer is CHECK THE SOLUTION.. (i)-[A], [B], [D], (ii)-[A], (iii)-[A], [B], [C], [D], (iv)-B], [C]
Sol. For pure rolling µ ≥  and f = 
BodyCondition on μFriction forceRingμ ≥ 3/43 NCylinderμ ≥ 1/42 NHollow sphereμ ≥ 3/1012/5 NSolid sphereμ ≥ 3/1412/7 Ν

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Column I	Column II
(i) If µ < 0.25 body which must not undergo pure rolling motion	[A] Ring
(ii) If µ 0.3 work done by friction must be negative for	[B] Hollow sphere
(iii) If µ = 0.4, total mechanical energy will be conserved for	[C] Solid sphere
(iv) If µ = 0.25, friction force will be 2N for	[D] Cylinder

Body	Condition on μ	Friction force
Ring	μ ≥ 3/4	3 N
Cylinder	μ ≥ 1/4	2 N
Hollow sphere	μ ≥ 3/10	12/5 N
Solid sphere	μ ≥ 3/14	12/7 Ν

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