Question

(II) A 0.72-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 15.0 s. What is the mass of the sphere

Answer 1

Answer:

$m = 23.3 kg$

Explanation:

As we know that it will have constant torque on it

so the acceleration of the ball will be constant so here we can say that we can use kinematics equation

$\theta = \omega_i t + \frac{1}{2}\alpha t^2$

$160(2\pi) = 0 + \frac{1}{2}\alpha (15^2)$

$320 \pi = 112.5 \alpha$

so we have

$\alpha = \frac{320\pi}{112.5}$

$\alpha = 8.94 rad/s^2$

now we know that

$\tau = I \alpha$

$10.8 = I(8.94)$

$I = 1.21 kg m^2$

so we know that

$I = \frac{2}{5}mR^2$

here we know that

diameter = 0.72 m

so radius (R) = 0.36 m

$\frac{2}{5}m(0.36^2) = 1.21$

$m = 23.3 kg$