A uniform 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 Fig. Match the following (most appropriate choice) :
(a)`mg//4 lt F lt mg//2` (i) Cube will move up.
(b) `F gt mg//2` (ii) Cube will not exhibit motion.
(c ) `F gt mg` (iii) Cube will begin to rotate and slip at `A`.
(d) `F = mg//4` (iv) Normal reaction effectively at `a//3` from A, no motion.

Options

A. `Ato2,Bto3,Cto1,Dto4`
B. `Ato1,Bto2,Cto3,Dto4`
C. `Ato4,Bto3,Cto2,Dto1`
D. `Ato3,Bto4,Cto1,Dto2`

Answer

A

Explanation

Cube has no motion if
`Fxxa=(mga)/2`
`:. F=(mg)/2`
Cube rotates when
`Fxxa gt mga/2`
`:. F gt (mg)/2`
When `(mg)/2 lt F lt (mg)/2` there is no motion
when `F.(mg)/2` cube moves
When `F gt mg` cube moves up
when `F=(mg)/2` no motion