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The gravitational potential at a height ...

The gravitational potential at a height 'h' above earth's surface is `-5.12xx10^(7)J//kg` and acceleration due to gravity at this point is `6.4ms^(-2)`. If R = 6400 km the value of h is : (Mass of object m=1 kg)

A

1200 km

B

1600 km

C

1800 km

D

2400 km

Text Solution

Verified by Experts

The correct Answer is:
B
Here P.E. `= -(GMm)/((R+h))`
`therefore` Gravitational potential `=-(GM)/((R+h))`
Also value of .g. at height .h.
`g.=(GM)/((R+h)^(2))`
`therefore ` Gravitational pentential
`V_(g)= -(g.(R+h)^(2))/((R+h))= -g.(R+h)`
`-5.12xx10^(7)=-6.4(6400+h)xx10^(3)`
where .h. is in kilometres.
`6400+h=(5.12xx10^(4))/(6.4)=8xx10^(3)=8000`
`h=1600km`.
Correct choice is (b).
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