How far from Earth must a body be along a line joining the sun to the earth so that resultage gravitational pull on the body due to Earth and sun is zero ? Distance between sun and the Earth is `1.5 xx 10^(8) km`. Mass of sun `= 3.25 xx 10^(5)` times mass of Earth.

Explanation

Let the body be at a distance x from the centre of earth.
Then its distance from centre of Sun = r - x
where r is the distance between the centre of sun and earth, its value is `1.5 xx 10^(11) m`.
As the gravitational pulls on the body due to earth and the sun are balanced out, we have
`(GM_(e)m)/(x^(2)) = (GM_(s)m)/((r-x)^(2))`
`rArr ((r-x)/(x))^(2) = (M_(S))/(M_(e)) = 3.3 xx 10^(5)`
`rArr (r-x)/(x) = sqrt(3.3 xx 10^(5)) = 574 rArr r - x = 574 x`
`rArr x = (r )/(575)`
`= (1.5 xx 10^(11))/(575)m`
`= 2.6 xx 10^(8)m`