Physics - Center of Mass Question with Solution | TestHub

PhysicsCenter of MassMomentum conservationMedium3 minQB

PhysicsMediumsingle choice

Passage / Comprehension

A large mass M is released from rest at the top of an inclined plane of angle $θ$ and friction coefficient $μ$ . At the same time, a pendulum consisting of a small mass m and (massless) string of length L is released at height L (horizontally). The large mass slides down the incline and smoothly onto the table, continues across the frictionless table, and collides with the pendulum's mass just as the pendulum has reached the bottom of its swing and is approaching the large mass. The two masses stick together after the collision.

What must the initial height h have been in order for the pendulum of the combined mass to complete the vertical circle in the counterclockwise direction? [Take $μ = 0$ and $M = 2 m$ ]

Options:

Answer:

Solution:

With $M = 2 m$ , the combined mass $3 m$ needs $v_{c} \geq 5 gL$ to complete the circle. Momentum: $2 m 2 g h - m 2 gL = 3 m v_{c}$ .

$2 2 g h = gL (2 + 35) \Rightarrow h = \frac{L ( 2 + 3 5 ) ^{2}}{8} .$

Answer: (A)

Stream:JEESubject:PhysicsTopic:Center of MassSubtopic:Momentum conservation

⏱ 3mℹ️ Source: QB

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