Question

A boy of mass 40kg ran up a flight of 50 steps, each 10cm high, in 5s. Find the power developed by the boy.
A. 440 W
B. 500 W
C. 400 W
D. 700 W

Answer 1

Hint: Power is defined as the rate of doing work. As the boy is moving up so the work done in this case is equal to the potential energy possessed by the boy, this potential energy per unit time gives the power developed by the boy.

Complete step-by-step answer:
Step1: As the power is equal to the rate of doing work. Since a boy is moving up, the work done in this case is equal to the potential energy of the body.
Potential energy of a body is given by-
\[P.E = mgh\] …………..(1)
Where m= mass of the body, g= acceleration due to gravity and h=height of body.
Height of one step = 10 cm
As the boy moves 50 steps up, so the total height covered by the boy is
 $h = 500{\text{ }}cm$
 $h = \dfrac{{500}}{{100}} = 5m$
As we know $g \simeq 10m/{s^2}$
Also given that mass of boy $m = 40kg$
Substituting all values in equation (1) we get,
\[
  P.E = 40 \times 10 \times 5 \\
  P.E = 8000J \\
\]
Step2: As we know Energy per unit time is power. Therefore,
$Power(P) = \dfrac{{Energy}}{{time}}$
Also given that time taken by the boy $t = 5s$
Put all values in above equation
 $
  P = \dfrac{{8000}}{5} \\
   \Rightarrow P = 400W \\
$
Which is power developed by the boy. Hence option (C) is the correct option.

The correct answer is option (C)

Note: Always remember that work done actually equals energy. So never confuse between work done and energy, while calculating power either if we write ‘energy per unit time’ or ‘work done per unit time’ both these statements are true.