# A body of 1 kg moves in a circle. At time=0 it moves with the velocity of 4 m/s and a force of 16 N is exerted on it. The force and the velocity share an angle of 60°. What is the velocity at t=1s and what is the radius of the circle?

Jan 17, 2018

Here,the force has to be applied in the shown direction,or else the body will not be able to move in a circle,because a component of this force will tend to act centrifugally and take it away from the centre.

so,if this $16 N$ force acts for 1 sec duration on the particle,its $\cos \theta$ component will be responsible for tangential acceleration,and change in its centripetal force should be due to its $\sin \theta$ component in order to help it moving in the circle.

So,tangential acceleration done is $\frac{16 \cos 60}{m}$ or,$8 \frac{m}{s} ^ 2$(as $m = 1$)

so,velocity in $1 \sec$ will be, $12 \frac{m}{s}$ (using $v = u + a t$ here, $u = 4 \frac{m}{s}$) and with this new velocity the body will move in a circle of constant radius,so centripetal force must be increased.

Now, this $16 \sin 60$ amount of force should be responsible for the change in its centripetal acceleration,
so,we can write, $16 \sin 60 = m \left({v}^{2} / r - {u}^{2} / r\right)$ (where $r$ is the radius of the circle)

solving we get, $r = 9.23 m$