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:

hope it will help u :D:)))))

Answer 2

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

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.

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

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

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

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

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 .

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