question_answer 48)

                  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) \[mg/4\,<F<mg/2\]	(i) Cube will move up.
(b) \[F>mg/2\]	(ii) Cube will not exhibit motion.
(c) \[F>mg\]	(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.

                                 

Answer:

                  (a)® (ii), (b) ® (iii), (c) ® (i) and (d) ®  (iv)                                 \[{{\tau }_{1}}=Fa\] (anticlockwise) and \[{{\tau }_{2}}=ma\,\left( \frac{a}{2} \right)\]  (clockwise) Cube will not exhibit motion if \[{{\tau }_{1}}={{\tau }_{2}}\] or \[F=\frac{mg}{2}\]                 Cube will rotate if \[{{\tau }_{1}}\,>\,{{\tau }_{2}}\] or \[F>\,\frac{mg}{2}\].