Question

A boy weighing 42kg climbs up a stair of 30 steps each 10cm high in 4 mins and a girl weighing 30kg does the same in 3 mins.

Compare :-
(i) The work done by them.
(ii) The power developed by them.​

Answer 1

Answer:

Work done and power developed by boy will be 1260 J & 5.25 watt respectively .

Work done and Power developed by girl will be 900 J & 5 watt respectively.

Explanation:

According to the Question

Firstly we calculate the Work done by boy and power developed by him .

As it is given ,boy weighing 42kg climbs up a stair of 30 steps each 10cm high in 4 mins .

Displacement of boy after 4min = 30×10 = 300cm = 3m

Time taken ,t = 4*60 = 240s

Calculating the work done by the boy.

• W = mgh

Substitute the value we get

➻ W = 42*10*3

➻ W = 420*3

➻ W = 1260 J

• Hence, the work done by the boy will be 1260 Joules.

Now, calculating the power developed by boy .

• P = W/t

substitute the value we get

➻ P = 1260/240

➻ P = 5.25 Watt

• Hence, the power developed by the boy will be 5.25 watts.

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Similarly,

It is given girl weighing 30kg does the same in 3 mins and the displacement is same .

Time taken ,t' = 3×60 = 180s

calculating the work done by Girl .

• W' = mgh

substitute the value we get

➻ W' = 30*10*3

➻W' = 900J

• Hence, the work done by the girl will be 900Joules.

Calculating the power developed by the girl.

• P' = W'/t'

Substitute the value we get

➻ P' = 900/180

➻ P' = 5 Watt

• Hence, the power developed by the girl will be 5 watts.

Answer 2

$\purple{ \huge{ \underline{\underline{ \bf Question : }}}}$

A boy weighing 42kg climbs up a stair of 30 steps each 10cm high in 4 mins and a girl weighing 30kg does the same in 3 mins.

Compare:-

(i) The work done by them.

(ii) The power developed by them.

$\purple{ \huge{ \underline{\underline{ \bf Answer : }}}}$

$\sf Height \: after \: climbing \: up \: stair \: = \: \: \: \: \\ \\ \sf Number \: of \: steps \times Height \: of \: steps \\ \\ \leadsto \sf30 \times 10 = 300 \: cm = 3 \: m \: \: \: \: \: \: \: \: \: \:$

$\boxed{ \bf Work \: Done = mgh} \\ \\ \boxed{ \bf Power = \frac{W}{t} } \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\red{ \underline{\bf\underline{ In \: Case \: of \: Boy : }}}$

Time = 4 minutes = 60*4 s = 240 s

$\sf Given \begin{cases} \sf Mass \: of \: boy \:(m) = 42 \: kg \\ \\ \sf Height(h) = 3 \: m \\ \\ \sf Time(t) = 240 \: s\end{cases}$

$\sf Work \: Done _{(boy)} = mgh \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf Work \: Done _{(boy)} = 42 \times 10 \times 3 \: J \\ \\ \color{skyblue} \sf Work \: Done _{(boy)} = 1260 \: J \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\sf Power_{(boy)} = \frac{W}{t} \: \: \: \: \: \: \: \\ \\ \sf Power_{(boy)} = \frac{1260}{240} \: \: \\ \\ \sf\color{skyblue} Power_{(boy)} =5.25 \: W$

$\huge{ \bold{ - - - - - - }}$

$\red{ \underline{\bf\underline{ In \: Case \: of \:Girl : }}}$

Time = 3 minutes = 60*3 s = 180 s

$\sf Given \begin{cases} \sf Mass \: of \: boy \:(m) = 30 \: kg \\ \\ \sf Height(h) = 3 \: m \\ \\ \sf Time(t) = 180 \: s\end{cases}$

$\sf Work \: Done _{(girl)} = mgh \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf Work \: Done _{(girl)} = 30 \times 10 \times 3 \: J \\ \\ \color{skyblue} \sf Work \: Done _{(girl)} = 900 \: J \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\sf Power_{(girl)} = \frac{W}{t} \: \: \: \: \: \: \: \\ \\ \sf Power_{(girl)} = \frac{900}{180} \: \: \: \\ \\ \color{skyblue}\sf Power_{(girl)} =5 \: W \: \: \:$

$\red{ \underline{ \underline{\bf{Compare :}}}}$

1.

• Work done by boy is more than work done by girl .
• Work Done by boy is 1260 J .
• Work Done by girl is 900 J .

2.

• Power developed by boy is more than power developed by girl .
• Power developed by boy is 5.25 W .
• Power developed by girl is 5 W .

The boy takes more time and have more mass than girl therefore work done and power developed by boy is more than girl .