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The ratio of the weight of a body on the...

The ratio of the weight of a body on the Earth’s surface to that on the surface of a planet is 9 : 4. The mass of the planet is `1/9` of that of the Earth. If ‘R’ is the radius of the Earth, then the radius of the planet is where n is ___________ . (Take the planets to have the same mass density)

A

`(R)/(9)`

B

`(R)/(4)`

C

`(R)/(3)`

D

`(R)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
`W_(1)=(GM_(1)m)/(R_(1)^(2)), W_(2)=(GM_(2)m)/(R_(2)^(2))`
`(W_(1))/(W_(2))=(M_(1))/(M_(2))((R_(2))/(R_(1)))^(2)`
`(4)/(9)=(1)/(9)((R_(2))/(R_(1)))^(2)implies(R_(1))/(R_(2))=(1)/(2)`
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