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Consider a heavenly body that has a mass twice that of the earth and a radius thrice that of the earth. What will be the weight of an object on this heavenly body, if its weight on the earth is $450 N$ ?

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200 N

100 N

500 N

300 N

answer is B.

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Detailed Solution

The weight of an object on the heavenly body that has a mass twice that of the earth and a radius thrice that of the earth will be

100 N,

if its weight on the earth is

450 N

.
We know that the acceleration due to the gravity

(g)

of the earth is

g_{e} = \frac{GM}{R^{2}}

Here,

G

is the universal gravitational constant

M

is the mass of earth

R

is the radius of earth
According to the given data,
Mass of the heavenly body

(M_{h}) = 2 M

….. (1)
The radius of the heavenly body

(R_{h}) = 3 R

…… (2)
So, acceleration due to gravity on the heavenly body is given by

g_{h} = \frac{G M_{h}}{{R_{h}}^{2}}

From (1) and (2), we get

g_{h} = \frac{G (2 M)}{{(3 R)}^{2}}

\Rightarrow g_{h} = \frac{2 MG}{9 {(R)}^{2}}

But

g_{e} = \frac{GM}{R^{2}}

So,

g_{h} = \frac{2 g}{9}

….. (3)
Now,

W_{e} = m g_{e}

.…(4)
And it is given that

W_{e} = 450 N

….(5)
Thus, the weight of an object on a heavenly body is given by

W_{h} = m {\times g}_{h}

From equation (3), we get

W_{h} = m \times \frac{2 g_{e}}{9}

\Rightarrow W_{h} = \frac{2 m g_{e}}{9}

But, from (4) and (5) we know that

m g_{e} = 450 N

\Rightarrow W_{h} = \frac{2 \times 450}{9}

W_{h} = 100

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