Question

Ram and Shyam are climbing a tree. Ram weighs $\text{50 kg}$ and Shyam weighs $\text{60 kg}$. Power spent by Ram and Shyam to climb the tree are in the ratio of $3:2$. What is the ratio of time taken by Ram and Shyam to climb the tree?

• A. 9:5
• B. 5:9
• C. 5:18
• D. 18:5

Answer 1

The correct option is B

5:9

Work done by a body of mass, $m$ in climbing a height, $h$ is given by $mgh$.

Let the mass of Ram be $m_1$ and the mass of Shyam be $m_2$.

Also, let the height reached by Ram and Shyam be $h$.

$\therefore$Work done by Ram $=m_{1}gh$

Work done by Shyam $=m_{2}gh$

Let the time taken by Ram to climb the tree be $t_1$ and the time taken by Shyam to climb the tree be $t_2$.
$\text{Power}=\frac{\text{work}}{\text{time}}$

$\therefore$ Power expended by Ram, $P_1=\frac{m_{1}gh}{t_1}$
Power expended by Shyam, $P_2=\frac{m_{2}gh}{t_2}$
$\frac{P_1}{P_2}$ = $\frac{m_{1}gh{t}_2}{m_{2}gh{t}_1}$
$\Rightarrow \frac{3}{2}=\frac{50t_2}{60t_1}$
$\Rightarrow \frac{t_1}{t_2}=10:18=5:9$