Question

Show that the weight of an object on the moon is 1/6 of its weight on the earth.

Answer 1

Step 1,

The weight of an object of mass m is given by,

W = mg

The acceleration due to gravity is given by,

$g=\frac{GM}{R^2}$

Where, M is the mass of the planet or satellite where ‘g’ is to be found and R is its radius.

Step 2,

For Moon,

$M_m=7.36\times {10}^{22}kg$

$R_m=1.74\times {10}^{6}m$

So, $g_m=\frac{G{M}_m}{R_m^2}$

For earth,

$M_e=5.98\times {10}^{24}kg$

$R_e=6.37\times {10}^{6}m$

So,

$g_e=\frac{G{M}_e}{R_e^2}$

Step 3,

Now,

$\frac{g_m}{g_e}=\frac{\left(M_m{R}_e^2\right)}{\left(M_e{R}_m^2\right)}$

Putting all the values we get,

$\frac{g_m}{g_e}=\frac{7.36\times {10}^{22}\times (6.37\times {10}^6{)}^2}{5.98\times {10}^{24}\times (1.74\times {10}^6{)}^2}$

$\frac{g_m}{g_e}=0.165$

=> $g_e=\frac{g_m}{0.165}\approx 6g_m$
Hence we can say, the weight of an object on the moon is 1/6 of its weight on the earth.