Calculate the acceleration produced in a 2 kg rock due to earth (Assume the mass of earth M=6 × 1024 kg, radius of earth(r) = 6.4 × 106 m).

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Calculate the acceleration produced in a $2 kg$ rock due to earth (Assume the mass of earth $M = 6 \times 10^{24} kg$ , radius of earth( $r$ ) = $6.4 \times 10^{6} m$ ).

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98

m/s2

9.8

m/s2

0.98

m/s2

980

m/s2

answer is B.

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Detailed Solution

The acceleration produced in a

2 kg

rock due to earth is

9.8 m / s^{2}

Given data and assumptions:
Mass of the rock,

m = 2 kg

Mass of the earth

M = 6 \times 10^{24} kg

Radius of earth,

(r) = 6.4 \times 10^{6} m

Universal gravitational constant,

G = 6.67 \times 10^{- 11} N m^{2} / {kg}^{2}

We can calculate the force experienced by the earth on the rock using the Universal Law of Gravitation.

F = \frac{GMm}{r^{2}}

\Rightarrow

F = \frac{6.67 \times 10^{- 11} \times 6 \times 10^{24} \times 2}{{(6.4 \times 10^{6})}^{2}}

\Rightarrow

F = 19.6 N

Dividing the force from the mass of the rock we get the acceleration produced in the rock

g = \frac{F}{m}

g = \frac{19.6}{2}

g = 9.8 m / s^{2}

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