Question

Suppose a planet exists whose mass and radius both are half those of the earth. Calculate the acceleration due to gravity on the surface of this planet.

Answer 1

Mass and radius both are half of those of the earth
g (acceleration due to gravity) = ?
G (gravitational constant) = 6.673 × 10⁻¹¹ Nm² kg⁻²
M (mass of new planet)= (5.98 × 10²⁴  kg)/2
R (radius of the earth) = (6.4 × 10⁶ m)/2
`g = (GM)/R^2`
= `(6.673 xx 10^-11 xx 5.98 xx 10^24 xx 4)/((6.4 xx 10^6)^2 xx 2)`
= `(6.673 xx 10^-11 xx 5.98 xx 10^24 xx 4)/(6.4 xx 6.4 xx 10^12 xx 2)`              `(10^(24-11)=10^13)`
= `(6.673 xx 5.98 xx 4 xx 10^14)/(6.4 xx 6.4 xx 10^12 xx 2)`  `(10^(13-12)=10)`
= `(6.673 xx 5.98 xx 4 xx 10)/(6.4 xx 6.4 xx 2)`
= `(159.61816 xx 10)/(6.4 xx 6.4 xx 2)`
= `1.9484 xx 10` = 19.5 N