A solid sphere of mass 1 ~kg rolls on a table with linear speed 2 ~m / s, find its total kinetic energy.

Data : M=1 ~kg, v=2 ~m / s The total kinetic energy of a rolling body, E=1 2 M v^2 (1+k^2 R^2 ) For a solid sphere, k^2=2 5 R^2 E & =1 2 M v^2 (1+2 5 )=1 2 7 5 M v^2 & =7 10 M v^2=7 10 1 2^2=7 4 10 =2.8 ~J

A solid sphere of mass 1 ~kg rolls on a table with linear speed 2…

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Question

A solid sphere of mass $1 \mathrm{~kg}$ rolls on a table with linear speed $2 \mathrm{~m} / \mathrm{s}$, find its total kinetic energy.

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Answer

Data : $M=1 \mathrm{~kg}, \mathrm{v}=2 \mathrm{~m} / \mathrm{s}$
The total kinetic energy of a rolling body,
$
E=\frac{1}{2} M v^2\left(1+\frac{k^2}{R^2}\right)
$
For a solid sphere, $k^2=\frac{2}{5} R^2$
$
\begin{aligned}
\therefore E & =\frac{1}{2} M v^2\left(1+\frac{2}{5}\right)=\frac{1}{2} \times \frac{7}{5} M v^2 \\
& =\frac{7}{10} M v^2=\frac{7}{10} \times 1 \times 2^2=\frac{7 \times 4}{10}=2.8 \mathrm{~J}
\end{aligned}
$

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