A body weighs 30 kg on the surface of the earth. The mass of the body on the planet is 19th of the mass of the body on the surface of the earth and the radius is half of the earth. The weight of the body on the planet is ____ N.

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A body weighs $30 kg$ on the surface of the earth. The mass of the body on the planet is $\frac{1}{9} th$ of the mass of the body on the surface of the earth and the radius is half of the earth. The weight of the body on the planet is ____ $N$ .

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Detailed Solution

A body weighs

30 kg

on the surface of the earth. The mass of the body on the planet is

\frac{1}{9} th

of the mass of the body on the surface of the earth and the radius is half of the earth. The weight of the body on the planet is

130.6

N

.
Acceleration due to gravity on the earth

= g

Acceleration due to gravity on the planet

= g ’

Mass of the body on the earth

m_{E} = 30 kg

Mass of the body on the planet

m_{P} = 30 kg

The radius of earth

= r

The radius of the planet

= r ’

{\Rightarrow m}_{P} = \frac{1}{9} m_{E}

\Rightarrow r ’ = \frac{1}{2} r

[Given]
W know that

\Rightarrow g = \frac{Gm}{r^{2}}

[G is gravitational constant]

\Rightarrow g = 9.8 m / s^{2}

…(1)

\Rightarrow g ’ = \frac{G m_{P}}{{r'}^{2}}

…..(2)

\Rightarrow g ’ = \frac{G (\frac{1}{9}) m_{E}}{\frac{1}{2} r^{}}

\Rightarrow g ’ = \frac{4}{9} \times 9.8

Weight of the body on the planet

= mg ’

Weight of the body on the planet

= 30 \times (\frac{4}{9}) \times 9.8

Weight of the body on the planet

= 130.6 N

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