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Earth's gravitational force causes an acceleration of $5.5 {ms}^{- 2}$ in a $2 kg$ mass somewhere in space. Which of the following is the acceleration due to earth's gravitational force to in a $3 kg$ mass at the same place?

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5.5 {ms}^{- 2}

5 {ms}^{- 2}

0 {ms}^{- 2}

55 {ms}^{- 2}

answer is A.

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Detailed Solution

The acceleration due to the gravitational force of earth in a

3 kg

mass at the same place will be

5.5 {ms}^{- 2}

.
The acceleration produced by the gravity of the earth does not depend on the mass of the object. So, the acceleration produced within the

3 kg

mass will be the same as that produced in

2 kg

the mass; that is, the acceleration produced is going to be

5.5 {ms}^{- 2}

.
As per Newton's universal law of gravitation we know that force of attraction between

2

bodies is given by

F = \frac{G m_{1} m_{2}}{r^{2}} . . . . . . . . . . . . . . . . . (a)

G

is the gravitational constant

m_{1}

is the mass of first body

m_{2}

is the mass of the second body

r

is the distance between two bodies
At the same time we know that

F = mg

\Rightarrow mg = \frac{GMm}{r^{2}}

\Rightarrow g = \frac{GM}{R^{2}} . . . . . . . . . . . . . . . . . . . . . . (i)

Gravitational constant

G = 6.67 \times 10^{- 11} {Nm}^{2} {kg}^{- 2}

Orbital radius of moon around earth

R

Mass of the earth

M

Gravity is

g

From (i), we can understand that the gravity

g

is nowhere dependent on the mass of the object, which is under the influence of the gravity of the earth.
Thus, the acceleration due to the gravitational force of the earth will be the same on a

3 kg

and

2 kg

mass at the same place.

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