A solid sphere of mass 0.1 kg and radius 2 cm rolls down an inclined p

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

Options:

A . 1.4 m/sec

B . 0.14 m/sec

C . 14 m/sec

D . 0.7 m/sec

Answer: Option A
:
A

v = \sqrt{\frac{2 g h}{1 + \frac{k^{2}}{R^{2}}}} = \sqrt{\frac{2 \times 9.8 \times l sin θ}{1 + \frac{2}{5}}} [A s \frac{k^{2}}{R^{2}} = \frac{2}{5}, l = \frac{h}{s i n θ} a n d sin θ = \frac{1}{10} g i v e n]

\Rightarrow v = \sqrt{\frac{2 \times 9.8 \times 1.4 \times \frac{1}{10}}{\frac{7}{5}}} = 1.4 m / s .

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