Question

Calculate the force of gravitation due to earth on a man weighing 100 kg standing on the ground? (mass of earth =6×1024kg, Radius of earth=6.4×103km).​

Answer 1

• Let the force of gravitation be f.

• G is the gravitational constant, G = 6.673 × 10^-11 Nm²/kg²

• Mass of man , m = 100 kg

• Mass of earth, M = 6 × 10²⁴ kg.

• Radius of earth , R = 6.4 × 10³ km

SI unit of length (radius) is m.

$1 \: km \: = {10}^{3} \: m \\ \\ 6.4 \times {10}^{3} \: km = 6.4 \times {10}^{3} \times {10}^{3} \: m \\ \\ r = 6.4 \times {10}^{6} m$

Force of gravitation,

$f = \dfrac{GMm}{ {R}^{2} } \\ \\ f = \dfrac{6.673 \times {10}^{ - 11} \times 6 \times {10}^{24} \times 100 }{ {(6.4 \times {10}^{6} )}^{2} } \\ \\ = \dfrac{6.673 \times 6 \times {10}^{15} }{6.4 \times 6.4 \times {10}^{12} } \\ \\ = \dfrac{6.673 \times 6}{6.4 \times 6.4} \times {10}^{3} \\ \\ f = 0.977 \times {10}^{3} \\ \\ f = 977 \: N$

The gravitational force is 977 N.

Answer 2

Answer:

Explanation:

Given :

• Mass of man (m) = 100 kg
• Mass of earth (M) = 6 × 10²⁴ kg
• Radius of earth (r) = 6.4 × 10³ km ⇒ 6.4 × 10⁶ m
• Gravitational constant (G) = 6.67 × 10-¹¹ Nm²/kg²

To Find :

• The force of gravitation, F

Formula to be used :

• F = GMm/r²

Solution :

Force of gravitation,

F = GMm/r²

⇒ F = 6.67×10-¹¹×6×10²⁴×100/(6.4 × 10⁶)²

⇒ F = 6.67 × 6 × 10¹⁵/6.4 × 6.4 × 10¹²

⇒ F = 6.67 × 6 /6.4 × 6.4 × 10³

⇒ F = 0.977 × 10³

⇒ F = 977 N

Hence, the force of gravitation is 977 N.