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How is the power related to the speed at...

How is the power related to the speed at which a body can be lifted ? How many kilograms will a man working at the power of 100 W, be able to lift at constant speed of `1 m//s vertically ? (g= 10 m//s^2)`

Text Solution

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Let a body of mass m be lifted to a height h is time t.
Work done in time t, i.e., `W = mgh`
Thus, power = `(W)/(t) = (mgh)/(t) = mg (h//t) = mg xx` speed
where `h//t` is the speed at which the body is being lifted.
Aliter : `P = F upsilon = mg xx` speed.
Since power = `mg xx` speed,
`m = (power)/(g xx speed) = (100W)/((10 m//s^2) (1m//s)) = 10 kg (as power = 100 W and speed = 1m//s)`
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