1.

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)`

Answer» Correct Answer - 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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