Question

A particle of mass m describe a circle of radius the centripetal acceleration of the particle is 4/r2 the momentum of the particle is

Answer 1

Acceleration of particle(centripetal) = 4/r^2
v^2/r = 4/r^2
v = 2/√r
Now , momentum = m×v
= m×2/√r
= 2m/√r

Answer 2

Answer:

Momentum, P= 2m/√r

Explanation:

Given:-

    Mass of particle= m

Centripetal Acceleration, Ac= 4/ r²

Now;-

We know by formula that;

                Ac = v²/r___(1)

But,          Ac = 4/ r²___(2)    [given]

Equating (1) and (2), we get;-

            v²/ r= 4/ r²

                v² = 4/ r

                 v = √4/√r

                 v = 2/ √r  ______(3)

Now, finding momentum;-

∵ Momentum, P= Mass (m) × Velocity (v)

∴             P = m × v

                P = m × 2/√r    [From (3)]

So,            P = 2m/ √r

Hence, the momentum of the particle is 2m/√r.

Hope it helps! ;-))