Question

A one rupee coin starting from rest rolls down a distance of $1 \, m$ on an inclined plane at an angle of $30^\circ $ with the horizontal. Assuming that $g=9.8$ $m \, s^{- 2}$ , the time taken is

• A. $0.68s$
• B. $0.6s$
• C. $0.5s$
• D. $0.7s$

Answer 1

Answer: (D)

$l=1m\text{,}\theta =30^{\text{o}}\text{,}\text{g}=9\text{.}81ms^{- 2}\text{,}\textit{t}=\text{?}$
$\text{K}^{2} = \frac{1}{2} \text{R}^{2}$
$a = \frac{9 \text{.} 8 1 \times \frac{1}{2}}{1 + \frac{1}{2}} = \frac{4 \text{.} 9 \times 2}{3}$
$\Rightarrow $ $l=\frac{1}{2}at^{2}$
$\Rightarrow 1=\frac{1}{2}\times \frac{4 \text{.} 9}{3}\times 2\times t^{2}$
$\Rightarrow t=\sqrt{\frac{3}{4 \text{.} 9}}=0\text{.}7s$