Question

A solid sphere of mass 0.1 kg and radius 2 cm rolls down an inclined plane 1.4m in length at an angle whose slope is 1/10. If sphere started from rest, its final velocity will be

• A. 1.4 m/sec
• B. 0.14 m/sec
• C. 14 m/sec
• D. 0.7 m/sec

Answer 1

The correct option is A 1.4 m/sec

$v=\sqrt{\frac{2gh}{1+\frac{k^2}{R^2}}}=\sqrt{\frac{2\times 9.8\times l\sin \theta }{1+\frac{2}{5}}}[As\frac{k^2}{R^2}=\frac{2}{5},l=\frac{h}{sin\theta }and\sin \theta =\frac{1}{10}given]$
$\Rightarrow v=\sqrt{\frac{2\times 9.8\times 1.4\times \frac{1}{10}}{\frac{7}{5}}}=1.4m/s.$