Question

If mass and radius of the Earth are $6.0\times {10}^{24}$ kg and $6.4\times {10}^6$ m respectively, calculate the force exerted by the Earth on a body of mass 1 kg.

• A. 9.8 and 1 respectively
• B. 9.8 and respectively
• C. and 9.8 respectively
• D. 9.8 for both

Answer 1

The correct option is B

9.8 and respectively

From Newton's law of gravitation, we know that the force of attaraction between the bodies is given by:
F = $\frac{G{m}_1{m}_2}{r^2}$
Here, $m_1$ = mass of Earth = $6.0\times {10}^{24}$ kg and $m_2$ = mass of the body = 1 kg
r = distance between the two bodies = radius of the Earth = $6.4\times {10}^6$ m
G = $6.67\times {10}^{-11}$ N$\frac{m^2}{k{g}^2}$
F = $\frac{6.67\times {10}^{-11}\times 6.0\times {10}^{24}\times 1}{{(6.4\times {10}^6)}^2}$ = 9.8 N