(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 :

Answer:

[tex]m = 23.3 kg[/tex]

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

[tex]\theta = \omega_i t + \frac{1}{2}\alpha t^2[/tex]

[tex]160(2\pi) = 0 + \frac{1}{2}\alpha (15^2)[/tex]

[tex]320 \pi = 112.5 \alpha[/tex]

so we have

[tex]\alpha = \frac{320\pi}{112.5}[/tex]

[tex]\alpha = 8.94 rad/s^2[/tex]

now we know that

[tex]\tau = I \alpha[/tex]

[tex]10.8 = I(8.94)[/tex]

[tex]I = 1.21 kg m^2[/tex]

so we know that

[tex]I = \frac{2}{5}mR^2 [/tex]

here we know that

diameter = 0.72 m

so radius (R) = 0.36 m

[tex]\frac{2}{5}m(0.36^2) = 1.21[/tex]

[tex]m = 23.3 kg[/tex]

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