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(D) Let the acceleration of the system be $a$. Since $M$ and $m$ are stationary with respect to $M_0$,the whole system moves with acceleration $a = \f

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none of these

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(D) Let the acceleration of the system be $a$. Since $M$ and $m$ are stationary with respect to $M_0$,the whole system moves with acceleration $a = \frac{F}{M_0 + M + m}$.For block $M$: The pseudo force $Ma$ acts to the right. The tension $T$ in the string pulls it to the right. So,$T = Ma$.For block $m$: The weight $mg$ acts downwards. The friction force $f = \mu N$ acts upwards,where $N$ is the normal force. The pseudo force $ma$ acts horizontally on $m$ against the vertical surface,so $N = ma$.For $m$ to be stationary,the vertical forces must balance: $f = mg \implies \mu N = mg \implies \mu(ma) = mg \implies a = \frac{g}{\mu}$.Substituting $a$ into the system equation: $\frac{F}{M_0 + M + m} = \frac{g}{\mu} \implies F = (M_0 + M + m) \frac{g}{\mu}$.Since this result is not among the options,the correct choice is $D$.

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 $\mu$. Find the value$(s)$ of $F$ for which $M$ and $m$ are stationary with respect to $M_0$.

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