Question

A particle is moving in a circular path with a constant speed. If $\theta$ is the angular displacement, then starting from $\theta =0,$ the maximum and minimum change in the linear momentum will occur when value of $\theta$ is respectively :

• A. ${45}^{\circ }and{90}^{\circ }$
• B. ${90}^{\circ }and{180}^{\circ }$
• C. ${180}^{\circ }and{360}^{\circ }$
• D. ${90}^{\circ }and{270}^{\circ }$

Answer 1

The correct option is C ${180}^{\circ }and{360}^{\circ }$

Initial momentum, $P_i=mv\hat{y}$

At $\theta ={180}^o$, momentum $P_1=-mv\hat{y}$

Change in momentum $\Delta P=P_1-P_i=-2mv\hat{y}$

At $\theta ={360}^o$, momentum $P_2=mv\hat{y}$

Change in momentum $\Delta P=P_2-P_i=0$