A) 1 :2
B) 2:5
C) 2:7
D) 5:7
Correct Answer: C
Solution :
Let m be the mass, r the radius of the sphere, let v and co be linear and angular velocities, in rolling down. Total KE = Linear KE + Rotational KE Total KE\[KE=\frac{1}{2}m{{v}^{2}}+\frac{1}{2}I{{\omega }^{2}}\] where, \[I\]is moment of inertia\[\left( I=\frac{2}{5}m{{r}^{2}} \right)\] Total \[KE=\frac{1}{2}m{{v}^{2}}+\frac{1}{2}\left( \frac{2}{5}m{{r}^{2}} \right)\frac{{{v}^{2}}}{{{r}^{2}}}\] Total \[KE=\frac{1}{2}m{{v}^{2}}+\frac{1}{5}m{{v}^{2}}\] Total \[KE=\frac{7}{10}m{{v}^{2}}\] Hence ratio \[\frac{\text{Rotational}\,\text{KE}}{\text{Total}\,\text{KE}}=\frac{\frac{1}{5}m{{v}^{2}}}{\frac{7}{10}m{{v}^{2}}}=2:7\]You need to login to perform this action.
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