Question

X climbs up a small hill in 10 minutes, Y takes only 7 minutes in going up the same hill. The weight of X is equal to the weight of Y and is 54 kg. Which of the following statements is true?
1. Y spends more power than X
2. Y does more work than X
3. X does more work than Y
4. X spends more power than Y

Answer 1

Correct Answer - Option 1 : Y spends more power than X

Concept:

Power: Power is work done per unit time.

 \(Power = \frac{ Work }{Time}\)

work done by the force is a product of force acted on body and displacement.

work = force x displacement

force = mass x gravitational acceleration

Calculation:

•  X and Y climbed the same hill therefore displacement is the same for both. 
• Their weight is also the same.
• therefore work done by X and Y is the same.   

The time taken by X and Y to climb the hill is 10 and 7 minutes respectively.

Let, P_X and P_Y are power spent by X and Y respectively.    

P_X  = W / 10

P_Y = W / 7

As denominator of P_X is bigger compared to P_Y.

PX <  PY   

This explains Y spends more power than X.

PHYSICAL QUANTITY	SYMBOL	UNITS	DIMENSIONS
POWER	P	W	[L2 M T-3]
WORK	W	J	[L2 M T-2]
FORCE	F	N	[L M T-2]