Question

A boy of mass $55kg$ runs up a flight of $40$ stairs, each measuring $0.15m$ in $5s$. Column II given numerical value for quantities describe in Column I, match them correctly.

Column 1	Column 2
Force acting on the boy	$550$
Work done by the boy	$3300$
Gain of potential energy by the boy	$33000$
Power developed by the boy	$220$

Answer 1

Step 1: Given information in the question:

1. Total mass $=55kg$
2. height of stairs $=0.15m$
3. Total height covered by the boy $=0.15\times 40=6m$

Step 2: force acting on the boy is

$$\begin{gathered} \Rightarrow F=mg \\ \Rightarrow F=55\times 10 \\ \Rightarrow F=550N \end{gathered}$$

Step 3: the work done by the body.

$$\begin{gathered} \Rightarrow P.E.=mgh \\ \Rightarrow P.E.=55\times 10\times 6 \\ \Rightarrow P.E.=3300J \end{gathered}$$

Step 4: Gain of potential energy by the boy

$$\begin{gathered} \Rightarrow P.E.=mgh \\ \Rightarrow P.E.=55\times 10\times 6 \\ \Rightarrow P.E.=3300J \end{gathered}$$

Step 5: Power developed by the boy

work done = potential energy

Therefore,

$$\begin{gathered} W=3300J \\ P.E.=3300J \end{gathered}$$

$$\begin{gathered} P=\frac{W}{t} \\ P=\frac{3300}{15} \\ P=220J{S}^{-1} \end{gathered}$$

Therefore, power developed by the boy $P=220J{S}^{-1}$

Hence, the correct answer is A-I, B-II, C-II, D-IV