Two men with weights in the ratio 4:3 run up a staircase in time in the ratio 12:11 . The ratio of the power of the first to that of second is

Question

Two men with weights in the ratio 4:3 run up a staircase in time in the ratio 12:11 . The ratio of the power of the first to that of second is (A) (4/3) (B) (12/11) (C) (48/33) (D) (11/9)

Tardigrade Admin · Accepted Answer

textPower=( textwork/ texttime)=( textenergy/ texttime)=( textitmgh/t)=(W h â¡/t) ( W = weight ) ∴ (P 1/P â¡2)=(W â¡1/W â¡2)× (t2/t1)=(4/3)× (1 1/1 2)=(1 1/9) ( h is same in both cases )

Q. Two men with weights in the ratio $4 : 3$ run up a staircase in time in the ratio $12 : 11$ . The ratio of the power of the first to that of second is

$\frac{4}{3}$

$\frac{12}{11}$

$\frac{48}{33}$

$\frac{11}{9}$

$Power = \frac{work}{time} = \frac{energy}{time} = \frac{mgh}{t} = \frac{Wh}{t}$ ( $W$ = weight )
$∴ \frac{P _{1}}{P _{2}} = \frac{W _{1}}{W _{2}} \times \frac{t _{2}}{t _{1}} = \frac{4}{3} \times \frac{11}{12} = \frac{11}{9}$ ( $h$ is same in both cases )

Q. Two men with weights in the ratio 4:3 run up a staircase in time in the ratio 12:11 . The ratio of the power of the first to that of second is

34​

1112​

3348​

911​