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

A uniform cube of mass m and side a is placed on a frictionless horizo

1.	A uniform cube of mass m and side a is placed on a frictionless horizontal surface. A vertical force Fis applied to the edge as shown in figure. Match the following (most appropriate choice).
Answer» Solution :Torque of force about point A is `tau=Fa` (anticlockwise) Torque of weight mg of cube about point A `tau_(2)=mg((a)/(2))` (CLOCKWISE) The cube will not exhibit just rotational MOTION if `tau_(1)=tau_(2)` or `F=(mg)/(2)` Cube will rotate if `tau_(1) gt tau_(2)or F gt (mg)/(2)` For normal reaction force acting effectively at a DISTANCE `(a)/(3)` from point A, the cube will just rotate if `mgxx(a)/(3)=Fa` or `F=(mg)/(3)` When `F=(mg)/(4) LT (mg)/(3)`, there will be no rotational motion So, we conclude that `(a) to (ii), (b) to (III), (c) to (i), d to (iv)`