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CBSE Class 9 Science Question 3 of 33

Gravitation — Question 3

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Question

Question 3

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 × 1024 kg and radius of the earth is 6.4 × 106 m.)

Answer

Mass of the body (m) = 1 kg

Mass of the earth (M) = 6 × 1024 kg

Radius of the Earth (R) = 6.4 × 106 m

G = 6.67 x 10-11 Nm2kg-2

According to the formula for gravitational force we know,

F = G MmR2\dfrac{\text{M}\text{m}}{\text{R}^2}

Substituting we get,

F=6.67×10−11×6×1024×1(6.4×106)2=6.67×10136.4×6.4×1012=9.77 N≈9.8 N\text{F} = \dfrac{6.67 \times 10^{-11}\times 6 \times 10^{24} \times 1}{(6.4 \times 10^6)^2} \\[1em] = \dfrac{6.67 \times 10^{13}}{6.4 \times 6.4 \times10^{12}} \\[1em] = 9.77 \text{ N} \approx 9.8 \text{ N}

Hence, magnitude of the gravitational force = 9.8 N