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  • A solid sphere of mass 1kg and radius 1m is projected with velocity 10m/s at t=0s on a rough horizontal surface. Find its rotational kinetic energy when the sphere starts rolling. <img al

A solid sphere of mass 1kg and radius 1m is projected with velocity 10m/s at t=0s on a rough horizontal surface. Find its rotational kinetic energy when the sphere starts rolling.

Option: 1

10.2 Joule


Option: 2

25.5 Joule


Option: 3

35.7Joule


Option: 4

50.0Joule


Answers (1)

best_answer

Conserving angular momentum about its point of contact .

mvr=mv_{c.m}r+I_{c.m}w\\v=v_{c.m}+\frac{2}{5}v_{c.m}\\v=\frac{7}{5}v_{c.m}\\v_{c.m}=\frac{5}{7}v=\frac{5}{7}\times10=\frac{50}{7}m/s\\K_{R}=\frac{1}{2}I_{c.m}w^{2}=\frac{1}{2}\times\frac{2}{5}mr^{2}w^{2}\\K_{R}=\frac{1}{5}mv_{c.m}^{2}\\K_{R}=\frac{1}{5}\times1\times\frac{50\times50}{7\times7}=\frac{500}{49}=10.2 Joule

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