Question

What will be the acceleration due to gravity on the surface of the moon, if its radius is
1/4th the radius of the earth and its mass is 1/80 times the mass of the earth

TNSCERT Class 10 Physics Ch 15 Laws of Motivation and Gravitation

Answer 1

acc due to gravity on earth g is given by formula g earth = GM/R^2 where G is universal gravitational constant M mass of earth R radius of earth for moon mass m = mass of earth/80= M/80 radius is r = radius of earth /4 = R/4 g of moon = Gm/r^2 put small m = M/80 and r= R/4 we get (R/4)^2 =R^2/16 g moon =16GM/80R^2 as we know GM/R^2 = g of earth so g moon = g of earth/5 ( g of earth is 9.8m/s^2 or u can say 10) so g moon = 10/5 g moon =2 ( which means 5 times less than that of g of earth)