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?

1 Answer
Jan 17, 2018

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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 16N force acts for 1 sec duration on the particle,its cosθ component will be responsible for tangential acceleration,and change in its centripetal force should be due to its sinθ component in order to help it moving in the circle.

So,tangential acceleration done is 16cos60m or,8ms2(as m=1)

so,velocity in 1sec will be, 12ms (using v=u+at here, u=4ms) and with this new velocity the body will move in a circle of constant radius,so centripetal force must be increased.

Now, this 16sin60 amount of force should be responsible for the change in its centripetal acceleration,
so,we can write, 16sin60=m(v2ru2r) (where r is the radius of the circle)

solving we get, r=9.23m