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Physics - Center of Mass Question with Solution | TestHub

PhysicsCenter of MassMomentum conservationHard2 minQB

PhysicsHardsingle choice

Passage / Comprehension

A small object of mass $m = 1 kg$ is released from rest at the top of an inclined plane that connects to a horizontal plane without an edge. it slides onto a cart of mass M that has a semi-cylindrical surface of radius $R = 0.36 m$ fixed to the middle of it, as shown in the figure. The small object reaches the topmost point of the semi-cylinder and stops there. It continues to move vertically with free fall and hits the cart exactly at the edge. All friction can be neglected.\\

At what height h was the small object released ?

Options:

Answer:

Solution:

Momentum conservation: $m v_{0} = M V$ ⇒ $v_{0} = \frac{M}{m} g R$ .

Slide from height $h$ : $v_{0}^{2} = 2 g h$ .

$h = \frac{v _{0}^{2}}{2 g} = \frac{1}{2} (\frac{M}{m})^{2} R$ - (B)

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

⏱ 2mℹ️ Source: QB

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