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

Answer:

Mass of the sphere is 19.2 kg

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 $\Theta =160revolution=160\times 2\pi =1004.8rad$

From second equation of motion

$\Theta =\omega _it+\frac{1}{2}\alpha t^2$

So $1004.8=0\times t+\frac{1}{2}\times \alpha \times 14^2$

$\alpha =10.25rad/sec^2$

Torque is given $\tau =10.8Nm$

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

So $10.8=10.25\times I$

$I=1.053kgm^2$

Moment of inertia of sphere is equal to $I=\frac{2}{5}Mr^2$

So $1.053=\frac{2}{5}\times M\times 0.37^2$

M = 19.23 kg

So mass of the sphere is 19.23 kg