Question

One man takes 1 min to raise a box to a height of 1 meter and another man takes half min. to do so. The potential energy in the two cases is
A. Different
B. Same
C. Energy of the first is more
D. Energy of the second is more

Answer 1

Hint: Recall the formula for gravitational potential energy of the body of mass m above the height h from the ground. Then check whether the term potential energy depends upon the time or not. Also, we can check which parameter depends upon the time.

Formula used:
\[P.E = mgh\]
Here, m is the mass of the box, g is the acceleration due to gravity and h is the height of the body from the ground.

Complete step by step answer:
We have given that the height to which the box is raised is the same for both the persons. Also, the mass of the box is also the same in both the cases.
We have the formula for gravitational potential energy of the object at a height 1 meter above the ground.
\[P.E = mgh\]
Here, m is the mass of the box, g is the acceleration due to gravity and h is the height of the box from the ground.
Since the above equation does not involve the term elapsed time. Therefore, the potential energy in both cases should be the same.

So, the correct answer is option (B).

Note:
 The potential energy does not depend on the time but the power depends upon the time. The power is work done per unit time. The work done is the change in potential energy of the box. Since the power is inversely proportional to the time, the power of the second person is greater than that of the first person. Also, the kinetic energy in the second case is greater than in the first case since the velocity of raising the box is more in the second case.