Match the following statements related to pure rolling motion with their correct descriptions or expressions. List - I List - II (P) Condition for pure rolling of a wheel of radius R (1) 0 (Q) Total k

Question

Match the following statements related to pure rolling motion with their correct descriptions or expressions.

List - I	List - II
(P) Condition for pure rolling of a wheel of radius R	(1) $0$
(Q) Total kinetic energy of a body of mass M and radius R undergoing pure rolling (K is radius of gyration)	(2) $v_{CM} = R ω$
(R) Velocity of the point of contact with the ground for a body in pure rolling	(3) $2 v_{CM}$
(S) Velocity of the topmost point of a wheel of radius R undergoing pure rolling, if its center of mass moves with speed $v_{CM}$	(4) $\frac{1}{2} M v_{CM}^{2} (1 + \frac{K ^{2}}{R ^{2}})$

TestHub · Accepted Answer

P. For pure rolling, the condition is that the velocity of the center of mass $v_{CM}$ is equal to $R ω$ .

Q. The total kinetic energy of a body undergoing pure rolling is the sum of its translational and rotational kinetic energies: $K E_{t o t a l} = \frac{1}{2} M v_{CM}^{2} + \frac{1}{2} I ω^{2} = \frac{1}{2} M v_{CM}^{2} (1 + \frac{K ^{2}}{R ^{2}})$ .

R. In pure rolling, the point of contact with the ground is instantaneously at rest, so its velocity is $0$ .

S. The velocity of the topmost point of a wheel in pure rolling is the sum of the center of mass velocity and the tangential velocity due to rotation: $v_{t o p} = v_{CM} + R ω = v_{CM} + v_{CM} = 2 v_{CM}$ .

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