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` (p) Cube will move up.
(b) `F gt mg//2` (q) Cube will not exhibit motion.
(c ) `F gt mg` (r) Cube will begin to rotate and slip at `A`.
(d) `F = mg//4` (s) Normal reaction effectively at `a//3` from A, no motion.

Options

A. A-p, B-q, C-s, D-r
B. A-r, B-s, C-q, D-p
C. A-q, B-r, C-p, D-s
D. A-s, B-p, C-r, D-q

Answer

C

Explanation

From the figure, Moment of force F about a,
`tau_(1)= F xx a`, anticlockwise.
Moment of weight Mg of cube about A,
`tau_(2)= Mg xx a/2`, clockwise.
The cube will not exhibit any motion, if `tau_(1)=tau_(2)`

or `F xx a = Mg xx a/2`or `F=(Mg)/(2)`
The cube will rotate only, when `tau_(1) gt tau_(2)`
`F xx a gt (Mga)/2` or `F gt (Mg)/(2)`
If we assume that normal reaction is effective at `a//3` from A, then block would turn if
`Mg xx a/3 =F xx a` or `F = (Mg)/(3)`
When `F=(Mg)/(4) lt (Mg)/3`, there will no motion.
Hence we conclude A-q, B-r, C-p, D-s.