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Step-by-Step Solution
Step 1: Understand the Physical Situation
Two coolies are raising the same suitcase (same mass) through the same height.
However, they take different times to do it. Thus, the work done in both cases is the same,
but the time taken is different.
Step 2: Recall the Definition of Power
Power $P$ is defined as the work done $W$ per unit time $t$:
$$P = \frac{W}{t}.$$
Step 3: Identify the Work Done
The work done by each coolie is given by
$$W = mgh,$$
where
$m$ is the mass of the suitcase,
$g$ is the acceleration due to gravity,
and $h$ is the height through which the suitcase is raised.
Since both coolies lift the same suitcase to the same height, $W$ is the same for both.
Step 4: Compare the Times
• The first coolie takes 1 minute (i.e., 60 s).
• The second coolie takes 30 s.
Step 5: Calculate the Ratio of Their Powers
Since $W$ (work done) is the same for both coolies, the ratio of their powers is inversely proportional to the ratio of the times taken:
$$\frac{P_1}{P_2} = \frac{\frac{W}{t_1}}{\frac{W}{t_2}} = \frac{t_2}{t_1}.$$
Substitute the given times:
$$\frac{P_1}{P_2} = \frac{30 \text{ s}}{60 \text{ s}} = \frac{1}{2}.$$
Therefore, the powers of the two coolies are in the ratio $1 : 2$.
Final Answer: 1 : 2
