# The value of acceleration due to gravity on the surface of Earth in cgs unit is-

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The value of acceleration due to gravity on the surface of Earth in cgs unit is-
1. 9.81 m/s2
2. 981 cm/s2
3. 9.81 cm/s2
4. 0.981 m/s2

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Correct Answer - Option 2 : 981 cm/s2

The correct answer is option 2) i.e. 981 cm/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:

• The cgs unit system is the metric system based on the centimetre as the unit of length, the gram as the unit of mass, and the second as the unit of time.
• We know that acceleration due to gravity on the surface of Earth is 9.81 m/s2.
• On appropriate conversion,

1 m = 100 cm

⇒ 9.81 m/s2 = 9.81 × 100cm/s2 = 981 cm/s2

• Thus, the value of acceleration due to gravity on the surface of Earth in the cgs unit is 981 cm/s2.