A block of dimensions lxtxh and uniform density `rho_(w)` rests on a rough floor. Wind blowing with speed V and of density `rho_(a)` falls perpendicularly on one face of dimension lxh of the block as shown in figure. Assuming that air is stopped when it strikes the wall and there is sufficient friction on the ground so that the block does not slide, the minimum speed V so that the block topples is :

Options

A. `((rho_(w)g)/(rho_(a)h))^(1//2) t`
B. `((rho_(a)g)/(rho_(w)h))^(1//2) t`
C. `(g/h)^(1//2) g`
D. None of these

Explanation

`F=V(dm)/(dt) =rho_(a)l hV.V=rho_(a)l h V^(2) { :. (dm)/(dt)=rho_(a)l hV}`
Total torque of air about point P is `rho_(a)lhV^(2) h/2`
`tau_(a)=(rho_(a)lh^(2)V^(2))/2, tau_(w)=Mg.1/2 =rho_(w)l.h.t.g t/2`
for toppling `tau_(a) gt tau_(w)rArr V gt((rho_(omega)g)/(rho_(A)h))^(1//2).t`