First slide

Gravitational force and laws

Question

If the mass of one particle is increased by 50% and the mass of another particle is decreased by50%, the force between them is

Easy

A

decrease by 25%
B

decrease by 75%
C

increase by 25%
D

does not change

Solution

$\begin{array}{l} F_{1} = \frac{G m_{1} m_{2}}{d^{2}} \\ F_{2} = G \frac{(m_{1} + \frac{m_{1}}{2}) (m_{2} - \frac{m_{2}}{2})}{d^{2}} = G \frac{(\frac{3 m_{1}}{2}) (\frac{m_{2}}{2})}{d^{2}} = \frac{3 G m_{1} m_{2}}{4 d^{2}} \\ F % = (\frac{F_{2}}{F_{1}} - 1) 100 = (\frac{\frac{3 F_{1}}{4}}{F_{1}} - 1) 100 = - \frac{1}{4} \times 100 = - 25 % \\ - i v e s i g n i n d i c a t e s d e c r e a s e \end{array} = \frac{3 F_{1}}{4}$

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