NEETPhysicsRotational Motion
A thin uniform rod, pivoted at O , is rotating in the horizontal plane with constant angular speed , as shown in the figure. At time t=0 , a small insect starts from O and moves with constant speed v , with respect to the rod towards the other end. It reaches the end of the rod at t=T and stops. The angular speed of the system remains throughout. The magnitude of the torque (| |) about O , as a function of time is be
Correct answer
1
Step-by-step solution
Angular momentum, | L | or L=I (about axis of rod) Moment of inertia of the rod-insect system. I=I_ rod +m x²=I_ rod +m v² t² Here, m= mass of insect L= (I_ rod +m v² t² ) Now | |= d L d t = (2 m v² t ) or | | t i.e. the graph is straight line passing through origin. After time T, L= constant | | or d L d t =0 i.e., when the insect stops moving, L does not change and therefore T becomes constant.