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A ball of mass2 kg and another of mass 4...

A ball of mass`2 kg` and another of mass `4 kg` are dropped together from a `60` feet tall building . After a fall of `30` feet each towards earth , their respective kinetic energies will be the ratio of

A

`sqrt(2):1`

B

`1:sqrt(2)`

C

`1:2`

D

`1:4`

Text Solution

Verified by Experts

The correct Answer is:
C
The realation between momentum (P) and kinetic energy (K) is given by `P^(2)=2km`
In this case, `P_(2)=(150)/(100)P_(1)=3/2P_(1)`
`therefore P_(2)^(2)/P_(1)^(2)=(2K_(2)m)/(2K_(1)m)=(K_(2))/(K_(1))`
`therefore K_(2)/K_(1)=((3/2P_(1)))/(P_(1)^(2)) =9/4 therefore K_(2)=9/4 K_(1)`
`K_2-K_(1)=5/4 K_(1)`
Percentage increase in K.E.
`=((K_(2)-K_(1))/(K_(1))) xx 100=((5/4K_(1))/(K_(1))) xx 100=125%`
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