Question

A particle of mass m moves in a circular path of radius r under the action of force which delivers it constant power p and increases its speed. The angular acceleration of particle at time (t) is proportional

Answer 1

Even though the particle is speeding up and the centripetal force required to keep it in the same circular path is increasing, no work is done by the centripetal force because it is perpendicular to the direction of motion of the particle. The only work done is in the direction of motion, causing acceleration, so we can think of this as a linear acceleration problem (initially). 

power P = force x speed in direction of force 
= mass x acceleration x speed 
= m(dv/dt)v 
where dv/dt is linear acceleration. 
power P is constant so 
vdv/dt = (P/m) 
(1/2)v^2 = (P/m)t. 
v = rw where w is angular velocity, and r is constant, so 
w^2 = (2P/mr^2)t 
w = ct^1/2 
where c is a constant. The angular acceleration is 
dw/dt = (1/2)ct^-1/2. 

Answer 2

Answer:

Answer is F.V >0

Explanation:

just see the uploaded photo