A lift raises 50 passengers each having average weight $600 \mathrm{~N}$ to a height of $100 \mathrm{~m}$ at…
A lift raises 50 passengers each having average weight $600 \mathrm{~N}$ to a height of $100 \mathrm{~m}$ at a constant speed in time $t$. If the average power of $15 \mathrm{~kW}$ is required by the lift, then the value of $t$ in seconds is
$150$
$100$
$300$
$200$
Solution
We know that, Power $=\frac{\text { Work done }}{\text { Time }}$
$\Rightarrow P=\frac{W}{t}=\frac{F \times s}{t}$
$\Rightarrow \quad P=\frac{m g h}{t}$ ...(i)
Here, weight of passengers $=m g=50 \times 600 \mathrm{~N}$
height, $h=100 \mathrm{~m}$
Power, $P=15 \mathrm{~kW}$
$=15 \times 1000 \mathrm{~W}$
So from eq. (i) we have,
$t=\frac{m g h}{P}$
$=\frac{50 \times 600 \times 100}{15 \times 1000}$
$\Rightarrow \quad t=200 \mathrm{~s}$