Question

A $50 kg$ man with $20 kg$ load on his head climbs up $20$ steps of $0.25 m$ height each. The work done by the man on the block during climbing is
A. $5 J$
B. $350 J$
C. $1000 J$
D. $3540 J$

Answer 1

Hint: The work done by force depends only on the initial and final position of the body. Here the work is done on the load by the gravitational force. Use the formula for work done by the force to solve this question.

Formula used:
Work done, \[W = mgh\]
Here, m is the mass, g is the acceleration due to gravity and h is the total vertical distance moved by the body.

Complete step by step answer:
We know that the work done by force depends only on the initial and final position of the body. In this question, the work is done by the gravitational force. We need to determine the work done on the load by the gravitational force.

Let’s calculate the distance moved by the load as follows. We have given the height of each step is 0.25m and there are 20 such steps. Therefore, the total height will be,
\[h = 20 \times 0.25 = 5\,{\text{m}}\]

We have the expression for the work done by the gravitational force,
\[W = mgh\]
Here, m is the mass, g is the acceleration due to gravity and h is the total height moved by the load.

Substituting 20 kg for m, \[10\,m/{s^2}\] for g and 5 m for h in the above equation, we get,
\[W = \left( {20} \right)\left( {10} \right)\left( 5 \right)\]
\[ \therefore W = 1000\,{\text{J}}\]

Therefore, the work done by the man on the load on his head is 1000 J.Hence, option C is the correct answer.

Note:The expression for the work done by the gravitational force is, \[W = mg\left( {{h_f} - {h_i}} \right)\], where, “f” and “i" represents final and initial height respectively. Here, we have assumed that the initial height of the load is close to the ground. To answer these types of questions, always remember, the path of the motion of the body does not change the work done. If the body follows the circular path and comes back to the same position, the work done is zero.