Question

A body of mass m kg is lifted by a man to a height of one meter in 30 sec. Another man lifts the same mass to the same height in 60 seconds, calculating the ratio of the work done by the two men.
A. 1:2
B. 1:1
C. 2:1
D. 4:1

Answer 1

Hint:In order to proceed with the problem, we have to understand the work done. The work done is defined as the change in the kinetic energy of the body. Here we are going to find the ratio of work done by using the kinetic energy of a body.

Formula used:
The expression of potential energy is,
\[P.E = mgh\]
Here, $m$ is the mass of the body, $g$ is the acceleration of the body and $h$ is the height.

Complete step by step solution:
Consider a given mass that is lifted to a height of 1m. Let us assume that its initial kinetic energy was equal to zero and the initial potential energy is also equal to zero.Therefore, after it was lifted the final kinetic energy also equals zero because it was just lifted, and the potential energy has raised to a value of,
\[P.E = mgh\]
\[\Rightarrow P.E = mg\]............(Since, \[h = 1\])

Therefore, the total change in energy when the mass is completely lifted is mg joules.
We can write the first and second cases as,
\[{\left( {\Delta E} \right)_{30S}} = mg\,{\rm{ }}J\]
\[\Rightarrow {\left( {\Delta E} \right)_{60S}} = mg\,{\rm{ }}J\]
As you can see both potential and kinetic energy does not depend on time and since the only work is being done by man. So, both of them are equal to the work done by the man on the block. Therefore, in both cases, the work done is the same and there will be a ratio of 1:1.

Hence, option D is the correct answer.

Note: As we all know that energy is the capacity to do work that is, every form of energy is work. Work done on the body is usually stored in the form of energy. In order to do more work, more energy is required.