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. `-6.67xx10^(-7)`
B. `-6.67xx10^(-10)`
C. `-13.34xx10^(-7)`
D. `-6.67xx10^(-9)`

Answer

A

Explanation

` m_1 =100kg,m_2=8100 kg`
Distance =1m
Distance of null point from 100 kg,
`x=-(d)/(sqrt((m_2)/(m_1))+1)=(1)/(sqrt(((8100)/(100))+1))`
`=(1)/(sqrt(81)+1)=(1)/(9+1)=(1)/(10)=0.1 m`
Gravitational potential is
`-G[(m_1)/(0.1)+(m_2)/(0.9)]=-6.67xx10^(-11)[(100)/(10^-1)+(8100)/(9xx10^-1)]`
`=-6.67 xx10^(-11)[1000+9000]`
`=-6.67 xx10^(-11)[10^4]`
`=-6.67 xx10^(-7)J//kg`.