Question

1. A sphere of 40 kg is attracted by another sphere of 15 kg with a force of 0.1 mg wt. Find the value of the
universal constant of gravitation if the centre of sphere are 20 cm apart.
​

Answer 1

Given

• Mass of Sphere₁ = 40 kg
• Mar of Sphere₂ = 15 kg
• Force = 0.1 mg wt
• Distance between the centers of the spheres = 20 cm = 0.2 m

To Find

• The value of Gravitational Constant

$\qquad$━━━━━━━━━━━━━━━━━━━━━━━

• We shall first convert the Force to Newton and then using the formula of Gravitational Force would give us our answer

$\dag\: \underline{\textsf{ Force Applied :}}$

$\sf\dashrightarrow Force = 0.1 \times 10^{-3} \times 980 \ dyne$

$\sf\dashrightarrow Force = 98\times 10^{-3} \ dyne$

$\dashrightarrow\underline{\boxed{\pink{\sf Force = 9.8\times 10^{-7} \ N}}}$

$\quad$━━━━━━━━━━━━━━

$\displaystyle\underline{\bigstar\:\textsf{According to the Question :}}$

$\sf\dashrightarrow F = G\dfrac{m_1m_2}{R^2}$

$\sf\dashrightarrow G = \dfrac{FR^2}{m_1m_2}$

$\sf\dashrightarrow G = \bigg\lgroup \dfrac{9.8 \times 10^{-7} \times 0.2^2}{40\times 15}\bigg\rgroup$

$\sf\dashrightarrow G = \dfrac{392}{60} \times 10^{-11}$

$\dashrightarrow\underline{\boxed{\pink{\sf G = 6.5\times 10^{-11} \ m^3/kg \ s^2}}}$