Question

A car of masses $1500$kg is lifted up a distance of $30$m by crane $A$ in $0.5$ minutes. The second crane $B$ does the same job in $1$ minute. The ratio of their powers is:

• A. $1:2$
• B. $2:1$
• C. $1:1$
• D. $1:4$
• E. $4:1$

Answer 1

Answer: (B)

$2:1$

Given, mass of the car(m)$=1500$kg
Height of car$\left(h_1\right)=30$m
Time taken by crane A in lifting the car $\left(t_1\right)=0.5$min
Time taken by crane B in lifting the car $\left(t_2\right)=1$min
We know that, $P=\frac{mgh}{t}$
$\therefore P\propto \frac{1}{t}$
Now, $\frac{P_1}{P_2}=\frac{t_2}{t_1}$
$\Rightarrow \frac{P_1}{P_2}=\frac{60}{30}$
$\therefore \frac{P_1}{P_2}=\frac{2}{1}$.