1.

If the mass of earth is eighty times the mass of a planet and diameter of the planet is one fourth that of earth, then acceleration due to gravity on the planet would be

Answer»

<P>7.8 m/`s^(2)`
9.8 m/`s^(2)`
6.8 m/`s^(2)`
2.0 m/`s^(2)`

Solution :Since gravitational acceleration on EARTH is defined as
`g_(e) = (GM_(e))/(R_(e)^(2)) ""`.... (i)
mass of planet is `M_(p) = (M_(e))/(80) ` & radius `R_(p) = (R_(e))/(4)`
So `g_(p) = (GM_(P))/(R_(P)^(2)) ""`.... (ii)
From (i) & (ii), we GET
`g_(P) = g_(e)" "(M_(p))/(R_(p)^(2)) xx (R_(e)^(2))/(M_(e)) = (g_(e))/(5) = 2 m//sec^(2) ("as g = 10m"//sec^(2))`


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