## Question

The weight of a person on the earth is 80 kg. What will be his weight on the moon? Mass of the moon = 7.34 × 10^{22}kg, radius = 1.75 × 10^{6} m and gravitational constant *G* = 6.67 × 10^{ –11} Nm^{2}/kg^{2}. What will be the mass of the person at the moon? If this person can jump 2 meter high on the earth, how much high can he jump at the moon? If he can walk 100 m in 1 minute on the earth, then how much will he walk in 1 minute on the moon?

### Solution

128 N, 80 kg, , 12 m (approx).

The weight (W) of the person on the earth is 80 kg-wt. Hence the mass (*m*) is **80 kg**. If *M* be the mass and *R* the radius of the moon, then the force of attraction exerted by the moon on the person is

This is the weight *W’* (say) of the person on the moon.

The mass (*m*) of the person on the moon will be 80 kg (as on the earth). Hence for the person standing on the moon the acceleration due to gravity due to the attraction of the moon will be

For the person standing on the earth the acceleration due to gravity due the earth is 9.8 N kg ^{–1}. Therefore, for a person standing on the moon the acceleration due to gravity as compared to that on the earth will be So the person can jump 6 times higher on the moon. Hence height of the jump on the moon = 6 × 2 = **12 m (approx)**.

In moving on a plane, *g* does not affect. Hence the person will walk on the moon also 100 m in 1 minute.

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