Show that weight of an object on moon is 1/6 of its weight on earth.(given :mass of earth = 5.98 * 10 raised to 24 kg,mass of moon 7.36 *10 raised to 22 kg radius of earth 6.37 * 10 raised to 6m radius of the moon 1.74 * 10 raised to 6m

The acceleration due to gravity is given by,

g = GM/R^{2}

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

For Moon,

M_{m} = 7.36 × 10^{22} kg

R_{m} = 1.74 × 10^{6} m

So, g_{m} = GM_{m}/R_{m}^{2}

For earth,

M_{e} = 5.98 × 10^{24} kg

R_{e} = 6.37 × 10^{6} m

So,

g_{e} = GM_{e}/R_{e}^{2}

Now,

g_{m}/g_{e} = (M_{m} R_{e}^{2})( M_{e} R_{m}^{2})

Plugging in the values we get,

g_{m}/g_{e} = 0.16

=> g_{e} = g_{m}/0.16 ≈ 6g_{m}

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