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

Two blocks of masses m and 4 m lie on a smooth horizontal surface connected with a spring in its natural length. Mass m is given velocity v₀ through an impulse as shown in figure. Which of the following is true about subsequent motion?

Options

  1. AKinetic energy is maximum in ground frame and centre of mass (CM) frame simultaneously.
  2. BValue of maximum and minimum kinetic energy is same in CM and ground frame.
  3. CMinimum kinetic energy is zero in CM frame but non-zero in ground frame.
  4. DMaximum and minimum kinetic energy of m in ground frame is, respectively, 1 2 m v₀^2 and zero

Correct answer

D. Maximum and minimum kinetic energy of m in ground frame is, respectively, 1 2 m v₀^2 and zero

Step-by-step solution

In both CM and ground frame, K _ is there, when x is zero in spring, which occurs simultaneously. v_ C M = m (v₀ )+0 5 m = v₀ 5 K_ C M = 1 2 m ( 4 v₀ 5 )^2+ 1 2 (4 m) ( v₀ 5 )^2= 2 5 m v₀^2K_ ground = 1 2 m v_ ^2K_ CM =0K_ ground = 1 2 (m+4 m) v_ C M ^2= m v₀^2 10 K_ m = 1 2 m v₀^2 (ground frame) K_ =0 (ground frame when energy is shared by spring and 4 m and m will reverse direction of motion).

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