A solid cylinder A of mass M rolls with velocity v on horizontal part of a freely translating smooth wedge B of mass M. The cylinder climbs the wedge and reaches maximum height h=v²/(pg). Find p.
Physics · Mixed Chapter
JEE Main Practice

Question

A solid cylinder A of mass M rolls with velocity v on horizontal part of a freely translating smooth wedge B of mass M. The cylinder climbs the wedge and reaches maximum height h=v²/(pg). Find p.

G1 Physics · Accepted Answer

Step 1: Horizontal momentum is conserved: Mv=(M+M)V at the turning point, hence V=v/2. Step 2: Initial translational KE of cylinder is ½Mv². The cylinder's rotational KE (¼Mv² for solid cylinder) is unchanged because wedge contact is smooth (no torque at contact). Step 3: Translational KE of the two bodies at highest position is ½(2M)(v/2)²=¼Mv². Step 4: Loss in translational KE =¼Mv² converts to Mgh. Hence h=v²/(4g) ⇒p=4.