Question

A body mass of 40 g is gravitational potential energy of 160 J on the ground. Given g = 10 m/s2, determine the value of the mass of the body

Answer 1

Potential Energy= Mass×Acceleration due to gravity×Height 
P=m×g×h
P=160J, g=10m/s², m=40g=$\frac{40}{1000}$ kg

Here height is unknown, 
So we can write,
$h= \frac{P}{m×g}$
h=$\frac{160×1000}{100×40}$
h=40m

Answer 2

g = G M / R^2     
      R = radius of planet earth    G = gravitational constant = 6.67*10^-11     
      M = mass of earth .  m = 40g    we have find M
P. E. = G M m / R  = 6.67*10^-11 M 0.040 /R  = 160 Joules
      =>  M = 26.68 * 10^14 R
P E / g = R  m   from formulas
   => 160 / 10 = R * 0.040  => R =  400 meters    => M = 400 * 26.68 * 10^14  kg