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(A) Let the acceleration of the system be $a = F / (M + m + M_0)$.For block $m$ to be stationary with respect to $M_0$,the normal force $N$ exerted by

Vedclass · Accepted Answer

If $F = 0$,the blocks cannot remain stationary.

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(A) Let the acceleration of the system be $a = F / (M + m + M_0)$.For block $m$ to be stationary with respect to $M_0$,the normal force $N$ exerted by $M_0$ on $m$ must provide the acceleration $a$. Thus,$N = ma$.The vertical forces on $m$ are gravity $mg$ downwards and friction $f$ upwards. For equilibrium,$f = mg$.Since $f \le \mu N$,we have $mg \le \mu (ma)$,which implies $a \ge g / \mu$.If $F = 0$,then $a = 0$,so $f = mg$ cannot be balanced,meaning the blocks cannot remain stationary. Thus,$(A)$ is correct.For $f = 0$,we need $mg = 0$,which is impossible. Thus,$(C)$ is incorrect.For a range of $F$ such that $a \ge g / \mu$,the blocks can remain stationary,not just for one unique value. Thus,$(B)$ is incorrect.Therefore,only statement $(A)$ is correct.

Imagine a situation in which the horizontal surface of block $M_0$ is smooth and its vertical surface is rough with a coefficient of friction $\mu$. Identify the correct statement$(s)$.

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