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Most Important Selected Qs for JEE AdvancedPhysicsCenter of Mass, Momentum and Collision

A small ball of mass m is placed in a circular tube of mass M and radius R in gravity free space. Friction is absent between tube and ball. Ball is given a velocity v ₀ as shown. Then,

Options

  1. APath of ball from centre of mass of system will be circular.
  2. BPath of ball from centre of mass of system will be elliptical
  3. CRadius of curvature of ball at the time of projection of ball is M R m+M
  4. DNormal force between tube and ball if M=2 m , at the time of projection of ball is 2 m V₀^2 3 R

Correct answer

D. Normal force between tube and ball if M=2 m , at the time of projection of ball is 2 m V₀^2 3 R

Step-by-step solution

From centre of mass of system ball and centre of tube moves in circular path. Radius of curvature of ball at the time of projection of ball is M R m+M Normal force between tube and ball if M=2 m , at the time of projection of ball is aligned & V_ c m = m V₀ m+M & N=m ( (V₀-V_ c m )^2 r₁ ) aligned

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