Question

Consider a special situtation in which both the faces of the block $M_0$ are smooth, as shown in adjoining figure. Mark out the correct statement(s)


(A) If $F=0$, the blocks $M$ and $m$ cannot remain stationary
(B) For one unique value of $F$, the blocks $M$ and $m$ remain stationary with respect to block $M_0$
(C) There exists a range of $F$ for which blocks $M$ and $m$ remain stationary with respect to block $M_0$
(D) Since there is no friction, therefore, blocks $M$ and $m$ cannot be in equillibrium with respect to block $M_0$

• A. $\text{Only Statement A is Correct}$
• B. $\text{Only Statement B is Correct}$
• C. $\text{Only Statement C is Correct}$
• D. $\text{Both Statement A and B are Correct}$

Answer 1

The correct option is D $\text{Both Statement A and B are Correct}$

(A) If F = 0, the block cannot remains stationary

If the force $F=0$, block $M_0$ will remain stationary but there will be acceleration in the system of masses $m$ and $M$ i.e. $a=\frac{mg}{m+M}$

(B) For one unique value of F, the blocks M and m remain stationary with respect to block $M_0$.

This case will arise when the pseudo force due to acceleration acting on $M$ will be equal to weight $mg$.