Laws of Motion — Question 1

As we know,

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

Given,

F = 10 N, when separation = R,

Hence,

F₁ = $\dfrac{\text {G M m}}{\text R^2}$ = 10 N     [Equation 1]

If separation = $\dfrac{\text R}{2}$ then,

Substituting the values in the formula above, we get,

$\text F_2 = \dfrac{\text {G M m}}{\big(\dfrac{\text R}{2}\big)^2} \\[0.5em] \text F_2 = \dfrac{4 \text {G M m}}{\text R^2} \\[0.5em]$

$\text F_2 = 4 \times \big(\dfrac{\text {G M m}}{\text R^2}\big)$    [Equation 2]

Substituting the value of equation 1 in equation 2 we get,

F₂ = 4 x 10 N = 40 N