A unifrom cube of mass m and side a is placed on a frictionless horizontal surface .A vertical force F is applied to the edge as shown in figure ,match the following (most appropriate choice )

Explanation

Consider the below diagram
Moment of the force F about point A `tau_(1)=Fxxa` (anti - clockwise )
moment of weight mg of the cube about point A ,
`tau_(2)=mg xx(a)/(2)` (clock wise )

Cube will not exhibit motion ,if ` tau_(1)= ta_(2)`
(`:'` in this case , both the torque will cancel the effect the effect of each other )
`thetefore "" fxxa= mg xx(a)/(2)implies F=(mg)/(2)`
Cube will roate only when ,`tau_(1)gt tau_(2)`
`Fxxa gt mgxx(a)/(2)implies Fgt(mg)/(2)`
Let normal reaction is acting at `(a)/(3)` from point A , then
`mgxx(a)/(3)=Fxxa or F=(mg)/(3)`
when `F=(mg)/(4)` which is less than `(mg)/(3)` ""`(Flt(mg)/(3))`
there will be no motion .
`therefore (a) to (ii) (b) to (iii) (c ) to (i) (d) to (iv)`