#### 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.

#### Solution

Mass and radius both are half of those of the earth

g (acceleration due to gravity) = ?

G (gravitational constant) = 6.673 × 10^{−11} Nm^{2} kg^{−2}

M (mass of new planet)= (5.98 × 10^{24} kg)/2

R (radius of the earth) = (6.4 × 10^{6} 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