Respuesta :
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 [tex]\omega _i=0rad/sec[/tex]
Time t = 14 sec
Angular displacement [tex]\Theta =160revolution=160\times 2\pi =1004.8rad[/tex]
From second equation of motion
[tex]\Theta =\omega _it+\frac{1}{2}\alpha t^2[/tex]
So [tex]1004.8=0\times t+\frac{1}{2}\times \alpha \times 14^2[/tex]
[tex]\alpha =10.25rad/sec^2[/tex]
Torque is given [tex]\tau =10.8Nm[/tex]
Torque is equal to [tex]\tau =I\alpha[/tex], here I is moment of inertia and [tex]\alpha[/tex] angular acceleration
So [tex]10.8=10.25\times I[/tex]
[tex]I=1.053kgm^2[/tex]
Moment of inertia of sphere is equal to [tex]I=\frac{2}{5}Mr^2[/tex]
So [tex]1.053=\frac{2}{5}\times M\times 0.37^2[/tex]
M = 19.23 kg
So mass of the sphere is 19.23 kg
