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 powers is

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

Answer 1

Answer: (B)

Given, mass of the car $\left(m\right)=1500 \, kg$
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, $P=\frac{m g h}{t}$
$\therefore P \propto \frac{1}{t}$
Now, $\frac{P_{1}}{P_{2}}=\frac{t_{2}}{t_{1}}$
$\Rightarrow \, \frac{P_{1}}{P_{2}}=\frac{60}{30}$
$\therefore \, \frac{P_{1}}{P_{2}}=\frac{2}{1}$