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A raindrop of mass 1g falling from a hei...

A raindrop of mass `1g` falling from a height of `1km` hits is the ground with a speed of `50 ms^(-1)`. Which of the following statements is correct? `("Taking" g= 10ms^(-2))`.

Text Solution

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Given, mass of the rain drop(m)=100g =`1xx10^(-3)kg`
Height of falling(h)=`1km=10^(3)m=g=10m//s^(2)`
Speed of the rain drop(v)=50m/s
(a) Loss of PE of the drop=mgh =`1xx10^(-3)xx10xx10^(3)=10J`
(b) Gain in KE of the drop=`(1)/(2)mv^(2)`
`(1)/(2)xx1xx10^(-3)xx(50)^(2)`
`=(1)/(2)=xx10^(-3)xx2500=1.250J`
(c ) No, gain in KE is not equal to the loss in its PE, because a part of PE is utilised in doing work against the viscous drag of air.
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