Question

A particle is moving in a circle of radius 1.5 m. Its speed
is increasing by 180 rev/minute in one minute. What is its
linear acceleration ?
(a) 0.25 m/s2
(b) 0.30 m/s2
(c) 0.39 m/s2
(d) 0.47 m/s2​

Answer 1

Answer:

v=Ω(angular velocity)*r

Linear acceleration=dv/dt=(dΩ/dt)*r

Now ,180 rev in 1 min means 3 rev or 6π radians in 1 sec

which is nothing but rate of change of Ω or dΩ/dt

Thus dΩ/dt=6π

Therefore linear accn=6π*1.5=9π m/s^2

Answer 2

Given,

Radius of the particle=1.5m

Speed is increasing by 180 rev/minute

To Find,

Linear acceleration of particle.

Solution,

So, for linear acceleration the formula is,

a=angular acceleration× radius

Then, angular acceleration,α=dω/dt
                                                  =2πf/dt
                                                  =(2π×180rev s^-1/60)/60sec
                                                   =π/10 rad/s^-2

So, acceleration ,a=π/10×1.5

                              =3π/20 m/s²

                              =0.47m/s²

Hence, linear acceleration of a particle is 0.47m/s²(Option D).