Chapter - 3 Gravitation

Q&A -Ask Doubts and Get Answers

Q
Gravitation

Question:

What is the magnitude of the gravitational force between the earth and a 1 kg object on its surface? (Mass of the earth is 6 	imes 10^{24} kg and radius of the earth is 6.4 	imes 10^{6} m.)

Answer:

According to the Universal law of gravitation, the force of attraction between two bodies is given by:

F = Gfrac{m_1m_2}{r^2}

Here

m_1 = mass of Earth = 6 	imes 10^{24} kg

m_2 = mass of the body = 1 kg

G = Universal gravitational constant = 6.67 	imes 10^{-11} Nm^2kg^{-2}

r = distance between the two bodies

Radius of Earth, r =  6.4 	imes 10^{6} m

By substituting all the values in the equation

F = Gfrac{m_1m_2}{r^2}

F = 6.67 	imes 10^{-11} 	imesfrac{6 	imes 10^{24} 	imes 1}{(6.4 	imes 10^6)^2}

F = 9.8 N

This shows that Earth exerts a force of 9.8 N on a body of mass 1 kg. The body will exert an equal force of attraction of 9.8 N on the Earth.


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