Question

Three identical point masses, each of mass $1kg$ lie in the x-y plane at points $(0,0),(0,0.2m)$ and $(0.2m,0)$. The gravitational force on the mass at the origin is

• A. $1.67\times {10}^{-9}(\hat{i}+\hat{j})N$
• B. $3.34\times {10}^{-10}(\hat{i}+\hat{j})N$
• C. $1.67\times {10}^9(\hat{i}-\hat{j})N$
• D. $3.34\times {10}^{10}(\hat{i}-\hat{j})N$

Answer 1

The correct option is A $1.67\times {10}^{-9}(\hat{i}+\hat{j})N$

Gravitational force $F=\frac{G{m}_1{m}_2}{r^2}$

Given: $r=.2m{m}_1=m_2=1kg$

Now force on object at O due to B, $F_1=\frac{6.67\times {10}^{-11}\left(1\right)\left(1\right)}{(.2{)}^2}\hat{i}=1.67\times {10}^{-9}\hat{i}$

Force on object at O due to A, $F_2=\frac{6.67\times {10}^{-11}\left(1\right)\left(1\right)}{(.2{)}^2}\hat{j}=1.67\times {10}^{-9}\hat{j}$

Hence net force $F=1.67\times {10}^{-9}(\hat{i}+\hat{j})N$