9. GRAVITATION
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पृथ्वी तथा उसकी सतह पर रखी किसी $1\, kg$ की वस्तु के बीच गुरुत्वीय बल का परिमाण क्या होगा ? (पृथ्वी का द्रव्यमान $6 \times 10^{24} kg$ है तथा पृथ्वी की त्रिज्या $6.4 \times 10^{6} m$ है )।

A

$8.9\, N$

B

$9.8\, N$

C

$5.3\, N$

D

$2.3\, N$

Solution

According to the universal law of gravitation, gravitational force exerted on an object of mass $m$ is given by

$F=\frac{G M m}{r^{2}}$

Where,

Mass of Earth, $M = 6 \times 10^{24}\, kg$

Mass of object, $m = 1 \,kg$

Universal gravitational constant, $G = 6.7 \times 10^{-11}\, Nm^2 \,kg^{-2}$

Since the object is on the surface of the Earth,

$r =$ radius of the Earth $(R)$

$r = R = 6.4 \times 10^6\, m$

Therefore, the gravitational force

$F=\frac{G M m}{r^{2}}=\frac{6.7 \times 10^{-11} \times 6 \times 10^{24} \times 1}{\left(6.4 \times 10^{6}\right)^{2}}=9.8\, N$

Std 9
Science

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