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 160 revolutions in 14.0 s.

1. What is the mass of the sphere?

Answer 1

Mass of the sphere is 19.2 kg

Step-by-step explanation:

We have given diameter of the sphere d = 0.74 m

So radius r = 0.37 m

Initial angular velocity
`\omega _i=0rad/sec`

Time t = 14 sec

Angular displacement
`\Theta =160revolution=160* 2\pi =1004.8rad`

From second equation of motion

`\Theta =\omega _it+(1)/(2)\alpha t^2`

So
`1004.8=0* t+(1)/(2)* \alpha * 14^2`

`\alpha =10.25rad/sec^2`

Torque is given
`\tau =10.8Nm`

Torque is equal to
`\tau =I\alpha`, here I is moment of inertia and
`\alpha` angular acceleration

So
`10.8=10.25* I`

`I=1.053kgm^2`

Moment of inertia of sphere is equal to
`I=(2)/(5)Mr^2`

So
`1.053=(2)/(5)* M* 0.37^2`

M = 19.23 kg

So mass of the sphere is 19.23 kg