A uniform solid cylinder of mass M and radius R rolls without slipping down an incline of angle θ . Match the following quantities related to its motion. List - I List - II (P) Acceleration of the cen

Question

A uniform solid cylinder of mass M and radius R rolls without slipping down an incline of angle θ . Match the following quantities related to its motion. List - I List - II (P) Acceleration of the center of mass (1) 3 2 ​ g sin θ (Q) Minimum coefficient of static friction required for pure rolling (2) 3 1 ​ tan θ (R) Speed of the center of mass after rolling a distance L along the incline, starting from rest (3) 3 4 ​ gL sin θ ​ (S) Total kinetic energy of the cylinder after rolling a distance L (4) M gL sin θ (5) 2 1 ​ M gL sin θ (6) 3 2 ​ M gL sin θ

TestHub · Accepted Answer

For a solid cylinder rolling without slipping down an incline, the equations are M g sin θ − f = M a CM ​ and f R = I α = ( 1/2 M R 2 ) ( a CM ​ / R ) = 1/2 M a CM ​ . From these, a CM ​ = 3 2 ​ g sin θ (P-1) and f = 3 1 ​ M g sin θ . The minimum coefficient of static friction is μ s ​ = f / ( M g cos θ ) = 3 1 ​ tan θ (Q-2). Using v CM 2 ​ = 2 a CM ​ L , v CM ​ = 3 4 ​ gL sin θ ​ (R-3). The total kinetic energy is K E = 1/2 M v CM 2 ​ + 1/2 I ω 2 = 3/4 M v CM 2 ​ = 3/4 M ( 3 4 ​ gL sin θ ) = M gL sin θ (S-4).

List - I	List - II
(P) Acceleration of the center of mass	(1) $\frac{2}{3} g sin θ$
(Q) Minimum coefficient of static friction required for pure rolling	(2) $\frac{1}{3} tan θ$
(R) Speed of the center of mass after rolling a distance $L$ along the incline, starting from rest	(3) $\frac{4}{3} gL sin θ$
(S) Total kinetic energy of the cylinder after rolling a distance $L$	(4) $M gL sin θ$
	(5) $\frac{1}{2} M gL sin θ$
	(6) $\frac{2}{3} M gL sin θ$

Physics - Rotation Question with Solution | TestHub

Options:

Doubts & Discussion

JEE Advanced 2027 (Class 12+)