Question

suppose a planet exist whose mass and radius both are half of the earth calculate the acceleration due to gravity on the surface of the planet

Answer 1

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Answer 2

As we know that the acceleration in earth is calculated by the formula (Gm)/(r^2) which equals 9.8m/s^2 where m is the mass of the earth and r is the radius of the earth.

now,

mass of that planet is half of earth so it's mass is (1/2)(m) and it's radius is half of earth so, it's radius is (1/2)(r)

we will use the same formula to find the gravitational acceleration of that planet
which equals

{ G (1/2)(m)}/ {(1/2)(r)}^2

= (Gm/2) ÷ (r^2 /4)

= 4Gm / 2r^2

= 2Gm/ r^2

= (Gm/ r^2 ) × 2

now, substitute for Gm/r^2 of earth

= 9.8 × 2

= 19.6m/s^2

so, the value of g on that planet will be 19.6m/s^2.