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Suppose the mass of the earth somehow increases by $10 %$ without any change in its size. Then weight of an object will

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Increase by

10 % .

Decrease by

10 % .

Remain the same.

None of these.

answer is A.

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Detailed Solution

Suppose the mass of the earth somehow increases by

10 %

without any change in its size. Then weight of an object will increase by

10 % .

“Weight is a measure of force acting on an object of mass

m

due to gravitational force, giving it an acceleration

g

”. Gravitational acceleration for a certain planet of mass

M

and radius

R

is given by the following relation:

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

Where

G

is the universal gravitational constant.
According to the given information, the mass of the planet has increased by 10% although its size (radius) remains the same. Since

g

is directly proportional to

M

, the gravitational acceleration of the earth will also increase by

10 %

.
Also, as the weight of a body is proportional to the ‘g’ as,

W = mg

Therefore, the weight of object will also increase by

10 %

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