Q74 / 90 · KVPY 2013 (SB/SX) · Physics
A solid sphere rolls without slipping, first horizontal and then up to a point $X$ at height $h$ on an inclined plane before rolling down, as shown.
The initial horizontal speed of the sphere is
The initial horizontal speed of the sphere is
- Correct answerA$\sqrt{10 \mathrm{gh} / 7}$
- B$\sqrt{7 g h / 5}$
- C$\sqrt{5 g h / 7}$
- D$\sqrt{2 g h}$
Solution
$m g h=\frac{1}{2} m v^{2}+\frac{1}{2} \frac{2}{5} m R^{2} \frac{v^{2}}{R^{2}}$
$m g h=\frac{7}{10} m v^{2}$
$v=\sqrt{\frac{10 g h}{7}}$
Hence, the correct answer is option: 'A'.