Question

A particle of mass $m$ moves along a circle of radius $R$. Find the modulus of the average vector of the force acting on the particle over the distance equal to a quarter of the circle, if the particle moves with constant tangential acceleration ${\omega }_{\tau }$, the initial velocity being equal to zero.

• A. $m{\omega }_{\tau }$
• B. $\frac{m{\omega }_{\tau }}{2}$
• C. $2m{\omega }_{\tau }$
• D. $\sqrt{2}m{\omega }_{\tau }$

Answer 1

The correct option is A $m{\omega }_{\tau }$

Initial momentum $P_i=0$
velocity of particle after time t :

$v=u+at$ where $a={\omega }_t$ and $u=0$

$v={\omega }_{t}t$

final momentum $P_f=m{\omega }_{t}t(-\hat{i})$
So , $|\Delta P|=m{\omega }_{t}t$
hence , $|<F>|=\frac{|\Delta P|}{t}=m{\omega }_t$