91Ó°ÊÓ

a) Mass of particle B,$m_B=1\text{ k²µ}$

b) Distance of particle A from origin,$x_A=0.2\text{ m(´Ú°ù´Ç³¾´Ú¾±²µ³Ü°ù±ð)}$

c) Distance of particle B from origin,$x_B=0\text{ m}$

d) Distance of particle C from origin,$x_C=0.4\text{m(fromfigure)}$

e) Gravitational constant,$G=6.67×{10}^{−11}\text{ N}â‹\dots {\text{m}}^{\text{2}}{\text{/kg}}^{\text{2}}$

Force between two masses can be calculated by using Newton’s law of gravitation. According to Newton’s law of gravitation, the force of two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

Formula:

Gravitational force, $F=\frac{GMm}{r^2}$ .......(i)

Using equation (i),Force between mass A & B can be written as:

$\begin{array}{c}{F}_{AB}=\frac{G{m}_A{m}_B}{{x_A}^2}\\ 4.17×{10}^{−10}\text{ â¶Ä‰N}=\frac{6.67×{10}^{−11}\text{ â¶Ä‰N}â‹\dots {\text{m}}^{\text{2}}{\text{/kg}}^{\text{2}}\text{ â¶Ä‰}×\text{ â¶Ä‰}{m}_A\text{ â¶Ä‰}×\text{ â¶Ä‰}1\text{ â¶Ä‰kg}}{{\left(0.2\text{ â¶Ä‰m}\right)}^2}\text{ â¶Ä‰}\\ m_A=0.25\text{ k²µ}\end{array}$

Hence, mass of the particle A is$0.25\text{ k²µ}$

Using equation (i), Force between mass B & C can be written as:

$\begin{array}{c}{F}_{BC}=\frac{G{m}_B{m}_C}{x^2}\\ 4.17×{10}^{−10}\text{ â¶Ä‰N}=\frac{6.67×{10}^{−11}\text{ â¶Ä‰N}â‹\dots {\text{m}}^{\text{2}}{\text{/kg}}^{\text{2}}×1\text{ â¶Ä‰â€‰kg }×\text{ â¶Ä‰}{m}_C}{{\left(0.4\text{ â¶Ä‰m}\right)}^2}\\ m_C=1\text{ k²µ}\end{array}$

Hence, mass of particle C is .$1\text{ k²µ}$