Q.

Consider a uniform rod of mass M= 4m and length L  pivoted about its center. A mass m moving with velocity  ν  making angle θ=π4  to the rod’s long axis collides with one end of the rod and sticks to it. The angular speed of the rod-mass system just after the collision is:

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a

327νL

b

37νL

c

372νL

d

47νL

answer is A.

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Detailed Solution

Moment of inertia of rod and mass system = I=4mL212+mL22Applying Conservation of Angular Momentum about O, ​Loi=Lof ⇒mVr Sinθ=Iω        ​⇒mV2×L2=4mL212+mL24×ω  ∵r=L2and θ=45° ⇒ω=6V72L=32V7L
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Consider a uniform rod of mass M= 4m and length L  pivoted about its center. A mass m moving with velocity  ν  making angle θ=π4  to the rod’s long axis collides with one end of the rod and sticks to it. The angular speed of the rod-mass system just after the collision is: