Question

Newton's law of gravitation states that every body in the universe attracts every other body with a force F that varies directly as the product of their masses (m1, m2) and inversely as the square of the distance d between them. If both masses are increased by 60% and the distance between them is halved, by what percent will the force of attraction increase?

Round your answer to the nearest integer.

By

Answer 1

according to Newton's law, force is directly proportional to product of masses and inversely proportional to square of seperation between them.

e.g., $F\propto\frac{m_1m_2}{d^2}$

or, $\frac{F}{F'}=\frac{m_1m_2}{m'_1m'_2}\frac{d'^2}{d^2}$

a/c to question,

both masses are increased by 60%.

so, new masses are ; m'1 = $1.6m_1$ and m'2 = $1.6m_2$ respectively.

and distance between them is halved.

so, new distance between them, r' = r/2 or 0.5r

now, $\frac{F}{F'}=\frac{m_1m_2}{1.6m_11.6m_2}\frac{(0.5r)^2}{r^2}$

= 1/(1.6)² × (0.5)²/1

= (0.5/1.6)²

= (1/3.2)²

= (5/16)²

= 25/256

or, F' = 256F/25 = 10.24F

% increase in F = (F' - F)/F × 100

= (10.24 - 1)F/1 × 100

= 9.24 × 100

= 924 %

hence, force increased by 924%.