Question

There are two bodies of masses 100000kg and1000kg separated by distance of 1m.At what distance from the smaller body the intensity of gravitational field will be zero?

Answer 1

Given:

Mass Of Body A =10^5 Kg =m2

Mass Of Body B = 10^3 Kg =m1

Here, In formula, g is gravitational constant not the acceleration of gravity.

Gravitational Field Intensity (g) =

$gm \div r ^{2}$

Gravitational Field. = Gravitational Field

Intensity Of Mass A Intensity Of Mass B

It will be equal because net gravitational Field Intensity is 0

$gm1 \div {x} ^{2} \: \: = gm2 \div ({r + x} ) ^{2}$

$\: (g \times {10}^{3} ) \div {x}^{2} \: = (g \times {10}^{5} ) \div {r + x}^{2}$

$( {r + x}^{2} ) \div {x}^{2} = {10}^{3} \div {10}^{5}$

${(r + x \div x)}^{2} = 10 ^{ - 2}$

$\sqrt{ {(r + x \div x})^{2} } = \sqrt{10 ^{ - 2} }$

$r + x \div x = 1 \div 10$

$10(r + x) = x$

$10r + 10x = x$

$9x = 10r$

$x = 10r \div 9$

Hence Gravitational Field will be zero at 10r÷9