The boides of masses 100 kg and 8100 kg are held at a distance of 1 m. The gravitational field at a point on the line joining at them is zero. The gravitational potential at the point in J/kg is `(G = 6.67 xx 10^(-11) Nm^(2 // kg^(2))`

Options

A. `-6.67 xx 10^(-7)`
B. `-6.67 xx 10^(10)`
C. `-13.34 xx 10^(7)`
D. `-6.67 xx 10^(-9)`

Answer

a

Explanation

Mass of first body `(m_(1)) = 100 kg`
mass of second body `(m_(2)) = 8100 kg`
distance between two bodies 1 m
Distance or null point from 100 kg
`x = (d)/(sqrt((m_(2))/(m_(1))) + 1)`
or `x = (1)/(sqrt((8100)/(100)) + 1)`
or, `x = (1)/(9 + 1) = (1)/(10)`
= 0.1 m
The gravitational potential at that point is given by
`= - G ((m_(1))/(0.1) + (m_(2))/(0.9))`
`= - 6.67 xx 10^(-11) ((100)/(10^(-1)) + (8100)/(9 xx 10^(-1)))`
`= - 6.67 xx 10^(-11) (1000 + 9000)`
`= - 6.67 xx 10^(-7) j//kg`