Question

One coolie takes 1 minute to raise a suitcase through a height of 2 m but the second coolie takes 30 s to raise the same suitcase to the same height. The powers of two coolies are in the ratio

• A. 1 : 3
• B. 2 : 1
• C. 3 : 1
• D. 1 : 2

Answer 1

The Correct Option is D

To find the ratio of the powers of the two coolies, we need to understand the relation between work, time, and power. Power is defined as the rate of doing work, and is given by the formula:

P = \frac{W}{t}

Where: P is the power, W is the work done, and t is the time taken to do the work.

Since both coolies raise the suitcase through the same height against gravity, the work done by each coolie is the same and is equal to:

W = m \cdot g \cdot h

where m is the mass of the suitcase, g is the acceleration due to gravity, and h is the height (2 m).

Let W be the work done. Since it is the same for both coolies, it can be ignored in the power ratio calculation:

P_1 = \frac{W}{t_1}
P_2 = \frac{W}{t_2}

Where:

• t_1 = 1\ \text{minute} = 60\ \text{seconds} (time taken by the first coolie)
• t_2 = 30\ \text{seconds} (time taken by the second coolie)

Thus, the ratio of their powers is given by:

\begin{align*} \frac{P_1}{P_2} &= \frac{\frac{W}{t_1}}{\frac{W}{t_2}} \\ &= \frac{t_2}{t_1} \\ &= \frac{30}{60} \\ &= \frac{1}{2} \end{align*}

The powers of the two coolies are therefore in the ratio 1:2.

Hence, the correct answer is 1:2.