Question

Easy Question:-

An old man and a young man both of mass 40 kg climb up of same height. While the old climbs up in 20 seconds, the boy climbs up in 10 seconds.Calculate the ratio of
the work done by them and their power.

Expected good content.
Thankyou.​

Answer 1

Ratio of work done by them :-

1 : 1

Ratio of their power :-

1 : 2

Explanation:

GIVEN :-

An old man's,

Mass = 40 Kg

Time taken to climb up a height = 20 sec

A young man's,

Mass = 40 kg...same as old man

Time taken to climb up same height climbed by old man = 10 sec

TO FIND :-

• Ratio of work done by them
• Ratio of their power

_______________________

SOLUTION :-

We know that,

$\bf work \:done = {E}_{f} - {E}_{i} \\ \bf P.E. = mgh$

Here,

E_f = Final Energy ; E_i = Initial Energy

P.E. = Potential Energy ; m = mass ; g = gravitational force ; h = height

$\:$

Because,

Here Initial Energy is 0.

So,

Work done = Final Energy = Potential Energy

$\:$

Now,

Work done by Old man = P E. = mgh

Work done by young man = P.E. = mgh

Because,

masses of both are same, gravitational force will always be same, height climbed up is same (A.T.Q.)

So,

Work done by Old man : Work done by Young man

=> mgh : mgh

[m, g & h are same. so, they will be cancelled]

$\bf = > \cancel{mgh} : \cancel{mgh} \\ \\ \bf = > \red { \boxed{ \bf \blue{1 :1}}}$

Hence,

Ratio of the work done by them = 1 : 1.

_______________________

Now,

$\bf power = \frac{work}{time}$

Because,

Work = P.E.

So,

Power of old man = $\bf \frac{P.E.}{t} = \frac{mgh}{20s}$

Power of young man = $\bf \frac{P.E.}{t} = \frac{mgh}{10s}$

So,

Ratio of their work -

$\bf \frac{mgh}{20s} : \frac{mgh}{10s}$

Both mgh s are same, so

$\bf \frac{ \cancel{mgh}}{20s} : \frac{ \cancel{mgh}}{10s} \\ \\ \bf = > \frac{1}{20} : \frac{1}{10} \\ \\ \bf = > \frac{1}{20} \times 20 : \frac{1}{10} \times 20 \\ \\ \bf = > \boxed{ \bf \green{ 1 : 2}}$

Hence,

Ratio of their powers is 1 : 2.

_____________________

Hope it helps.

#BeBrainly :-)