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 revolution…

Question

asked Jan 26, 2021 202k views

1 Answer

Blue Robin · Answer 1 · 2021-01-31T09:56:43+0000

Answer:

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