Question

A solid sphere of mass $0.1kg$ and radius $2cm$ rolls down an inclined plane $1.4m$ in length (slope 1 in 10). Starting from rest its final velocity will be

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

Answer 1

Answer: (A)

$1.4m/\sec$

Answer 2

$v = \sqrt{\frac{2gh}{1 + \frac{k^{2}}{R^{2}}}} = \sqrt{\frac{2 \times 9.8 \times l\sin\theta}{1 + \frac{2}{5}}}$

[As $\frac{k^{2}}{R^{2}} = \frac{2}{5}$, $l = \frac{h}{\sin\theta}$ and $\sin\theta = \frac{1}{10}$ given]

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