Question

for no change in the mass of the earth if its radius is halved the weight of an object of mass 10kg will bee how much?

Answer 1

Answer:

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Answer 2

Given,

radius of earth = 6400 km

mass of the object = 10 kg

To find,

Weight of object if the radius is halved

Solution,

We know that mass is a base quantity and does not depend on any factors. Hence it will be constant.

The gravitation acceleration of the earth is calculated using the following formula:

g = GM/R²

9.8 m/s² = GM/R²                                                                       (i)

where 'G' is the Gravitational constant, 'M' is the mass of Eartha and 'R' is the radius of Earth.

However the radius of Earth is halved.

∵ g' = GM/(R/2)²

g' = GM/(R²/4)

g' = 4 × GM/R²

Using equation (i)

g' = 4 × 9.8 m/s²

g' = 39.2 m/s²

Weight of object = mass × gravitational acceleration

W = m × g'

W = 10 kg × 39.2 m/s²

W = 392 kg m/s²

An object of mass 10 kg will weight 392 kg m/s² if the radius of the Earth is halved.