A 1 kg mass placed at a certain location in outer space experiences an acceleration of 6 m/s2 due to the earth's gravitational force. What will be the

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A 1 kg mass placed at a certain location in outer space experiences an acceleration of 6 m/sdue to the earth's gravitational force. What will be the acceleration of a 6 kg mass at the same place?

1. 36 m/s2
2. 6 m/s2
3. 3 m/s2
4. 1 m/s2

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Correct Answer - Option 2 : 6 m/s2

The correct answer is option 2) i.e. 6 m/s2

CONCEPT:

• Law of Universal Gravitation: It states that all objects attract each other with a force that is proportional to the masses of two objects and inversely proportional to the square of the distance that separates their centres.

It is given mathematically as follows:

$F = \frac{Gm_1m_2}{R^2}$

Where m1 and m2 are the mass of two objects, G is the gravitational constant and R is the distance between their centres.

• From the Law of Universal Gravitation, the gravitational force acting on an object of mass m placed on the surface of Earth is:

$F = \frac{GMm}{R^2}$

Where R is the radius of the earth.

From Newton's second law, F = ma = mg

$⇒ mg =\frac{GMm}{R^2}$

⇒ Acceleration due to gravity, $g =\frac{GM}{R^2}$

EXPLANATION:

We know that acceleration due to gravity, $g =\frac{GM}{R^2}$

• Clearly, g depends on the mass of the planet (M) and not on the mass of the object that experiences acceleration due to gravity.
• Therefore, the acceleration of the 6 kg mass at the same place is 6 m/s2 itself.