Question

A man carries a load of $50\,kg$ through a height of $40\,m$ in $25$ seconds. If the power of the man is $1568\,W$, his mass is:
A. 5 kg
B. 1000 kg
C. 200 kg
D. 50 kg

Answer 1

Hint: in order to solve the question, we will first use the relation between power, work done and the time after then we substitute the work done with the potential energy as the man is taking the load at heigh by substituting the physical quantities we will arrive at the answer

Formula used:
${\text{power}} = \dfrac{{{\text{work done }}}}{{{\text{time}}}}$
$P.E = mgh$
Where, $P.E$ is the potential energy, $M$ is mass, $g$ is gravitational constant and $h$ is height.

Complete step by step answer:
In the question we are given: A man carries a load through a height. If the power of the man is given, we have to find what his mass is.
Mass of load = 50 kg
Height of carrying the load = 40 m
Time to carry the load = 25 seconds
Power of the man = 1568 W
We will use the formula of power to find the mass of the man
${\text{power}} = \dfrac{{{\text{work done }}}}{{{\text{time}}}}$
Work done in this case is the potential energy as the load is taken up at height because there is difference in height hence it creates the potential energy
Formula of potential energy
$P.E = mgh$

Now we will substitute the potential energy in place of work done
${\text{power}} = \dfrac{{{\text{mgh}}}}{{\text{t}}}$
mass used in the formula is the collective mass of load and mass of man
$m = {m_{load}} + {m_{man}}$
Now we will substitute the value of m
${\text{power}} = \dfrac{{{m_{load}} + {m_{man}} \times {\text{g}} \times {\text{h}}}}{{\text{t}}}$
Now we will substitute the value of power, g, h, t, mass of load
Value of g = $10m{s^{ - 2}}$
$1568 = \dfrac{{50 + {m_{man}} \times 10 \times 40}}{{25}}$
Solving for mass of man
$\therefore {m_{man}} = 50\,kg$

Hence, the correct option is D.

Note: Many of the students will may mistake that kinetic energy is not taken into the consideration this is because we assume that load is moving at negligible speed which makes kinetic energy inconsiderable when we compare it with the potential energy of the load and man.