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 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
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For equal work, less time means more power.
Updated On: May 2, 2026
- 1 : 2
- 2 : 1
- 1 : 1
- 1 : 4
- 4 : 1
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The Correct Option is B
Solution and Explanation
Concept:
Power is the rate at which work is done:
\[
P = \frac{W}{t}
\]
Work done in lifting:
\[
W = mgh
\]
Step 1: Work done by both cranes: \[ W = 1500 \times g \times 30 \] This is same for both cranes.
Step 2: Time conversion: \[ t_A = 0.5 \text{ min} = 30 \text{ s}, \quad t_B = 60 \text{ s} \]
Step 3: Power ratio: \[ \frac{P_A}{P_B} = \frac{W/t_A}{W/t_B} = \frac{t_B}{t_A} \] \[ = \frac{60}{30} = 2 \] Final Answer: \[ P_A : P_B = 2 : 1 \]
Step 1: Work done by both cranes: \[ W = 1500 \times g \times 30 \] This is same for both cranes.
Step 2: Time conversion: \[ t_A = 0.5 \text{ min} = 30 \text{ s}, \quad t_B = 60 \text{ s} \]
Step 3: Power ratio: \[ \frac{P_A}{P_B} = \frac{W/t_A}{W/t_B} = \frac{t_B}{t_A} \] \[ = \frac{60}{30} = 2 \] Final Answer: \[ P_A : P_B = 2 : 1 \]
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