Question

A 0.74-m-diameter solid sphere can be rotated about an axis through its center by a torque of 10.8 m∗N which accelerates it uniformly from rest through a total of 150 revolutions in 16.0 s . What is the mass of the sphere? Express your answer to two significant figures and include the appropriate units.

Answer 1

Here,

let the mass of the sphere is m

let the angular acceleration is a

0.50 * a * t^2 = angle

0.50 * a * 16^2 = 150 * 2pi

a = 7.36 rad/s^2

Now, for the sphere

Using second law of motion

torque = I * a

10.8 = 2/5 * m * (0.74/2)^2 * 7.36

solving for m

m = 26.8 Kg

the mass of the sphere is 26.8 Kg