A ball of density ais released from rest from the centre of an accelerating sealed cubical vessel completely filled with a liquid of density `rho`. If the trough moves with a horizontal acceleration `veca_(0)` find the initial acceleration of the ball.

Answer

`ghatj`

Explanation

There are two net hydorstatic forces along `x` and `y` direction

`F_(bx)=Vrhoa_(0)=ma_(x)`, where` m=Vsigma`
or `a_(x)=(rho)/(sigma)a_(0)`
`F_(y)=Vrhog-mg=ma_(y)`
where `m=Vsigma`
`a_(y)=((rho)/(sigma)-1)g`
Then `veca=(rho)/(sigma)a_(0)hati+((rho)/(sigma)-1)ghatj`