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6.System of Particles and Rotational Motion
hard
The speed of a homogeneous solid sphere after rolling down an inclined plane of vertical height $h$, from rest without sliding, is
A
$\sqrt {\frac{{10}}{7}gh} $
B
$\sqrt {gh} $
C
$\sqrt {\frac{6}{5}gh} $
D
$\sqrt {\frac{4}{3}gh} $
(AIPMT-1992)
Solution
For solid sphere $I=\frac{2}{5} m R^{2}$
$Work-energy$ theorem, $m g h=\frac{1}{2} I w^{2}+\frac{1}{2} m v^{2}$
$m g h=\frac{1}{2} \times \frac{2}{5} m R^{2} w^{2}+\frac{1}{2} m v^{2}$ where $v=R w \quad$ (due to pure rolling)
$\Longrightarrow v=\sqrt{\frac{10}{7} g h}$
Standard 11
Physics
