Question:
A lift raises 50 passengers each having average weight \(600\ \text{N}\) to a height of \(100\ \text{m}\) at a constant speed in time \(T\). If the average power of \(15\ \text{kW}\) is required by the lift, then the value of \(T\) in seconds is
A lift raises 50 passengers each having average weight \(600\ \text{N}\) to a height of \(100\ \text{m}\) at a constant speed in time \(T\). If the average power of \(15\ \text{kW}\) is required by the lift, then the value of \(T\) in seconds is
Show Hint
Average power is calculated using
\[
P=\frac{W}{T}.
\]
For lifting bodies vertically, work done is equal to total weight multiplied by height.
Updated On: Jun 26, 2026
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The Correct Option is D
Solution and Explanation
Step 1: Calculate the total weight lifted.
Weight of one passenger is \[ 600\ \text{N} \] Number of passengers is \[ 50 \] Therefore, total weight is \[ 50 \times 600 = 30000\ \text{N} \]
Step 2: Calculate the work done by the lift.
The lift raises the passengers through a height \[ h=100\ \text{m} \] Work done is \[ W = \text{force} \times \text{displacement} \] So, \[ W = 30000 \times 100 \] \[ W = 3000000\ \text{J} \]
Step 3: Use the formula for power.
Average power is given by \[ P=\frac{W}{T} \] Given, \[ P=15\ \text{kW}=15000\ \text{W} \] Thus, \[ 15000=\frac{3000000}{T} \]
Step 4: Solve for \(T\).
Rearranging, \[ T=\frac{3000000}{15000} \] \[ T=200\ \text{s} \]
Step 5: Final conclusion.
Therefore, the time taken by the lift is \[ \boxed{200\ \text{s}} \]
Weight of one passenger is \[ 600\ \text{N} \] Number of passengers is \[ 50 \] Therefore, total weight is \[ 50 \times 600 = 30000\ \text{N} \]
Step 2: Calculate the work done by the lift.
The lift raises the passengers through a height \[ h=100\ \text{m} \] Work done is \[ W = \text{force} \times \text{displacement} \] So, \[ W = 30000 \times 100 \] \[ W = 3000000\ \text{J} \]
Step 3: Use the formula for power.
Average power is given by \[ P=\frac{W}{T} \] Given, \[ P=15\ \text{kW}=15000\ \text{W} \] Thus, \[ 15000=\frac{3000000}{T} \]
Step 4: Solve for \(T\).
Rearranging, \[ T=\frac{3000000}{15000} \] \[ T=200\ \text{s} \]
Step 5: Final conclusion.
Therefore, the time taken by the lift is \[ \boxed{200\ \text{s}} \]
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