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.\\

What is the ratio of mass of cart and mass of the particle ?

Options:

Answer:

Solution:

Energy: $\frac{1}{2} m v_{0}^{2} = 2 m g R + \frac{1}{2} M V^{2}$ , with $v_{0} = \frac{M}{m} g R$ and $V = g R$ .

$(\frac{M}{m})^{2} = 4 + \frac{M}{m}$ ⇒ $k^{2} - k - 4 = 0$ .

$k = \frac{1 + 17}{2}$ - (A)

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

⏱ 2mℹ️ Source: QB

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