Two bodies of mass 100 kg and 10^4 kg are l | vedclass

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(C) Let the distance from the $100 \ kg$ mass where the gravitational field intensity is zero be $x$. At this point,the gravitational field due to bot

Vedclass · Accepted Answer

$\frac{1}{11} \ m$

Vedclass · Answer

(C) Let the distance from the $100 \ kg$ mass where the gravitational field intensity is zero be $x$. At this point,the gravitational field due to both masses must be equal in magnitude and opposite in direction. Let $m_1 = 100 \ kg$ and $m_2 = 10^4 \ kg$. The distance between them is $d = 1 \ m$. The condition for zero gravitational field is: $\frac{G m_1}{x^2} = \frac{G m_2}{(d - x)^2}$ Taking the square root on both sides: $\frac{\sqrt{m_1}}{x} = \frac{\sqrt{m_2}}{d - x}$ Rearranging for $x$: $x = \frac{d \sqrt{m_1}}{\sqrt{m_1} + \sqrt{m_2}}$ Substituting the values: $x = \frac{1 	imes \sqrt{100}}{\sqrt{100} + \sqrt{10^4}} = \frac{10}{10 + 100} = \frac{10}{110} = \frac{1}{11} \ m$.

Two bodies of mass $100 \ kg$ and $10^4 \ kg$ are lying one meter apart. At what distance from the $100 \ kg$ body will the intensity of the gravitational field be zero?

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