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Consider a hypothetical planet which is ...

Consider a hypothetical planet which is very long and cylinderical. The density of the planet is `rho`, its radius is `R`.

If an object is projected radially outwards from the surface such that it reaches upto a maximum distance of `3R` from the axis then what should be the speed of projection?

A

`Rsqrt(2/3pirhoG)`

B

`2Rsqrt(pirhoGln3)`

C

`Rsqrt(4/3pirhoG)`

D

`Rsqrt(2/3pirhoGln3)`

Text Solution

Verified by Experts

The correct Answer is:
B
Work done by gravitational force, `W=-2piGrhoR^(2)mint_(R)^(3R)1/rdr`
`rArr E=-2piGrhomR^(2)ln3`.
Applying work energy theorem, we get
`-1/2mv^(2)=-2piGrhomR^(2)ln3 v=2Rsqrt(pirhoGln3)`
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