Question

A planet ‘P’ has a mass 2 times and radius 3 times that of the Earth. What is the acceleration due to gravity on the planet, if the acceleration due to gravity on the Earth is 10 m/s2.

Answer 1

`\sf\\\textsf{Let 'R' be the radius and 'm' be the mass of the Earth. Then, 2m and 3R will be}\\\textsf{the mass and radius of the planet respectively.}`

`\sf\\\textsf{Given,}\\\textsf{Acceleration due to gravity on earth(g)=10m/s}^2\\\textsf{Acceleration due to gravity on the planet}(g_p)=?`

`\sf\\\textsf{Now,}\\\textsf{g = }(GM)/(R^2)\\\textsf{or, }10=(GM)/(R^2)............(1)`

`\sf\\And,\ g_p=(G(2M))/((3R)^2)\\\\\textsf{or, }g_p=(2GM)/(9R^2)......(2)`

`\textsf{Here, G is called the Universal Gravitational Constant.}`

`\sf\\\textsf{Dividing equation(2) by (1),}\\(g_p)/(10)=(2GM/9R^2)/(GM/R^2)\\\\\textsf{or, }g_p/10=(2)/(9)\\\\\textsf{or, }g_p=(20)/(9)m/s^2\\`