Question

A car of mass $1500\,kg$ 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 power is

• A. 1:02
• B. 2:01
• C. 1:01
• D. 1:04

Answer 1

Answer: (B)

2:01

Answer 2

Given, mass of the car $(m)=1500 \,kg$
Height of $\text{car}\left(h_{1}\right)=30\, m$
Time taken by crane $A$ in lifting the $\operatorname{car}\left(t_{1}\right)=0.5\,\min$.
Time taken by crane $B$ in lifting the $\operatorname{car}\left(t_{2}\right)=1 \min$
We know that, $P=\frac{m g h}{t}$
$\therefore P \propto \frac{1}{t}$
Now, $\frac{P_{1}}{P_{2}}=\frac{t_{2}}{t_{1}}$
$\Rightarrow \frac{P_{1}}{P_{2}}=\frac{60}{30}$
$\therefore \frac{P_{1}}{P_{2}}=\frac{2}{1}$