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Three particles are projected vertically upward from a point on the surface of the earth with velocities (2gR/3),(gR),(4gR/3) respectively where R is the radius of the earth and g is the acceleration due to gravity on the surface of the earth. The maximum heights attained are respectively h1,h2,h3

A
h1:h2=3:4
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B
h2,h3=3:4
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C
h1,h3=1:4
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D
h2=R
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Solution

The correct option is A h1:h2=3:4
Solution:-
At maximum height, KE=0 so,
KEi=12mv2, Ui=GMmR
KEf=0, Uf=GMmg
As grating is a conservative
force,
KEi+Ui=KEf+Uf
12mv2GmmR=GMmh
h=GMm12mv2GMmR=GMGMRV22
So, h1=GMGMR12(2GM3R)2/2=32R
h2=GMGMR12(GMR)2/2=2R
h3=GMGMR12(4GM3R)2/23R
h1:h2=3:4,h2:h3=2:3 and h1:h3=1:2

1156140_1182131_ans_5742781a55af4a39949f1c5aa12a9502.jpg

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