Question

A one rupee coin starting from rest rolls down a distance of $1m$ 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)

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