Question

what is the force of gravity on a body of mass 150 kg lying on the surface of the earth mass of the earth is equal to 6 into 10 power 24 kg radius is equal to 6.4 into 10 power 6 meter



give the answer in full explanation ​

Answer 1

AnswEr :

• Force of gravity on a body = 1465.57 N.

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Explanation :

We are given with the mass of body, mass of earth and distance between them, that is,

• Mass of body, M = 150 kg.

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• Mass of earth, m = 6 × 10²⁴ kg.

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• Distance between them, R = 6.4 × 10⁶ m.

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• And, G = 6.67 × 10⁻¹¹ N m²/kg².

We have to find out the force of gravity on a body.

We know that, if we are given with mass of body, mass of earth and distance between them and universal gravitation force then we have the required formula, that is,

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$\sf{:\implies F = \dfrac{GMm}{r^2}}$

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Substituting the given values in the formula :

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$\sf{:\implies F = \dfrac{6.67 \times {10}^{ - 11} \times 6 \times {10}^{24} \times 150}{(6.4 \times {10}^{6})^2} }$

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$\sf{:\implies F = \dfrac{6.67 \times {10}^{ - 11} \times 6 \times {10}^{24} \times 15 \times 10}{{6.4}^{2} \times {10}^{12}} }$

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$\sf{:\implies F = \dfrac{6.67 \times 6 \times 15 \times {10}^{ - 23} \times {10}^{25} }{{6.4}^{2}} }$

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$\sf{:\implies F = \dfrac{6.67 \times 6 \times 15 \times {10}^{ - 23 + 25}}{{6.4}^{2}} }$

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$\sf{:\implies F = \dfrac{6.67 \times 6 \times 15 \times {10}^{2}}{{6.4}^{2}} }$

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$\sf{:\implies F = \dfrac{40.02 \times 15 \times {10}^{2}}{{6.4}^{2}} }$

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$\sf{:\implies F = \dfrac{600.3 \times {10}^{2}}{{6.4}^{2}} }$

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$\sf{:\implies F = \dfrac{600.3 \times 100}{{6.4}^{2}} }$

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$\sf{:\implies F = \dfrac{60030}{{6.4}^{2}} }$

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$\sf{:\implies F = \cancel{\dfrac{60030}{40.96} }}$

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$\sf{:\implies \boxed{\pink{\frak{F = 1465.57}}}}$

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Hence, the Force of gravity on a body is 1465.57 N.

Answer 2

Answer:

Given :-

• Mass of earth = 6 × 10²⁴ kg
• Radius of earth = 6.4 × 10⁶ m
• G = 6.7 × 10-¹¹ Nm²/kg²
• Mass of the body = 150 kg

To Find :-

• What is the force of gravity.

Formula Used :-

$\boxed{\bold{\large{F\: =\: \dfrac{GMm}{{r}^{2}}}}}$

where,

• F = Gravitational force
• G = Gravitational constant
• M = Mass of earth
• m = Mass of body
• r = Radius of earth

Solution :-

Given :

• G = 6.7 × 10-¹¹ Nm²/kg²
• M = 6 × 10²⁴
• m = 150 kg
• r = 6.4 × 10⁶

According to the question by using the formula we get,

⇒F = $\dfrac{6.7 \times {10}^{-11} \times 6 \times {10}^{24} \times 150}{(6.4 \times {10}^{6})^{2}}$

⇒F = $\dfrac{6.7 \times {10}^{-11} \times 6 \times {10}^{24} \times 150}{6.4 \times 6.4 \times {10}^{12}}$

⇒F = $\dfrac{6.7 \times 6 \times 15 \times {10}^{14}}{6.4 \times 6.4 \times {10}^{12}}$

⇒F = 14.72 × 10²

➠ F = 1472 N

$\therefore$ The force of gravity is 1472 N .