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A particle hanging from a massless sprin...

A particle hanging from a massless spring stretches it by `2 cm` at the earth's surface. How much will the same particle stretch the spring at a height Of `2624Km` from the surface of the earth? (Radius of the earth`=6400 km`)

A

1cm

B

2cm

C

3cm

D

4cm

Text Solution

Verified by Experts

The correct Answer is:
A
`g_(1) =(GM)/((R+h)^(2))`
`:. (g_(1))/(g) = ((R)/(R+h))^(2) :. g_(1) = ((R)/(R+h))^(2)g`
`g_(1) = ((6400)/(6400 +2624))^(2) xx g = (g)/(2)`
`:'` At surface of earth, `mg = kx_(0)`
At the height `h = 2624km, mg_(1) = kx`
`:. (x)/(x_(0)) = (g_(1))/(g)`
`:. x = (g_(1))/(g) xx x_(0) = (1)/(2) xx 2 = 1cm`
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