Three particles of mass 1 , kg each are place | vedclass

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Question

(A) Let the particle at the origin be $A(0,0)$,the particle at $(0.2, 0)$ be $C$,and the particle at $(0, 0.2)$ be $B$. All masses $m = 1 \, kg$.The g

Vedclass · Accepted Answer

$1.67 	imes 10^{-9} (\hat{i} + \hat{j}) \, N$

Vedclass · Answer

(A) Let the particle at the origin be $A(0,0)$,the particle at $(0.2, 0)$ be $C$,and the particle at $(0, 0.2)$ be $B$. All masses $m = 1 \, kg$.The gravitational force exerted by particle $C$ on $A$ is:$\vec{F}_{AC} = \frac{G m_A m_C}{r_{AC}^2} \hat{i} = \frac{6.67 	imes 10^{-11} 	imes 1 	imes 1}{(0.2)^2} \hat{i} = \frac{6.67 	imes 10^{-11}}{0.04} \hat{i} = 1.6675 	imes 10^{-9} \hat{i} \approx 1.67 	imes 10^{-9} \hat{i} \, N$The gravitational force exerted by particle $B$ on $A$ is:$\vec{F}_{AB} = \frac{G m_A m_B}{r_{AB}^2} \hat{j} = \frac{6.67 	imes 10^{-11} 	imes 1 	imes 1}{(0.2)^2} \hat{j} = 1.67 	imes 10^{-9} \hat{j} \, N$The net force on particle $A$ is:$\vec{F}_{net} = \vec{F}_{AC} + \vec{F}_{AB} = 1.67 	imes 10^{-9} (\hat{i} + \hat{j}) \, N$

$(a)$ Gravitational constant $(G)$	$(i)$ $[L^{2}T^{-2}]$
$(b)$ Gravitational potential energy	$(ii)$ $[M^{-1}L^{3}T^{-2}]$
$(c)$ Gravitational potential	$(iii)$ $[LT^{-2}]$
$(d)$ Gravitational intensity	$(iv)$ $[ML^{2}T^{-2}]$

Three particles of mass $1 \, kg$ each are placed at $(0, 0)$,$(0, 0.2 \, m)$,and $(0.2 \, m, 0)$. What is the net gravitational force on the particle placed at the origin?

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