A thin shell of mass m and radius R is fixed. Two particles of same mass m are fixed at point A and B on the shell such that AB subtends an angle of `120^(@)` at the centre. A particle of mass m is held at point C inside the shell which is on perpendicular bisector of line AB. Find the velocity of mass at C when it reaches the opposite end of the point C on the shell under the influence of gravitational field.

Answer

`[(4Gm)/(R )(1-(1)/(sqrt(3)))]^(1//2)`

Explanation

`(AC)/(sin 120^(@))=(R )/(sin30^(@))`
`AC=sqrt(3)R`
`U_(i)+K_(i)=U_(f)+K_(f) AC' = R`
`U_("shell")+(-Gm^(2))/(sqrt(3)R)-(Gm^(2))/(sqrt(3)R)+0=(-Gm^(2))/(R )-(Gm^(2))/(R )+(1)/(2)mv^(2)+U_("shell")`
`v=[(4Gm)/(R )(1-(1)/(sqrt(3)))]^(1//2)`