Question

a planet of volume v and mass M is gravitational acceleration G on its surface if it expands 8 times its original volume what will be the acceleration due to gravity​

Answer 1

let x is the radius of the planet.

so,volume of the planet, v = 4/3πx³

now, volume of the planet becomes 8 times its original volume.

so, v' = 8v

⇒4/3πR³ = 8 × 4/3πx³

⇒R³ = 8x³

⇒R = 2x .......(1)

initial gravitational acceleration = g

using formula, g = GM/r²

initial acceleration, g = GM/x²

......(2), [ here, initial radius of the planet is x ]

so, final gravitational acceleration,g' = GM/R²

= GM/(2x)²

= GM/4x²

from equation (2),

g' = g/4

hence, acceleration will be 1/4th of its initial value. i.e., g/4

Answer 2

$\huge\bold\purple{Answer:-}$

let x is the radius of the planet.

so,volume of the planet, v = 4/3πx³

now, volume of the planet becomes 8 times its original volume.

so, v' = 8v

⇒4/3πR³ = 8 × 4/3πx³

⇒R³ = 8x³

⇒R = 2x .......(1)

initial gravitational acceleration = g

using formula, g = GM/r²

initial acceleration, g = GM/x²

......(2), [ here, initial radius of the planet is x ]

so, final gravitational acceleration,g' = GM/R²

= GM/(2x)²

= GM/4x²

from equation (2),

g' = g/4

hence, acceleration will be 1/4th of its initial value. i.e., g/4