91Ó°ÊÓ

The given data can be listed below as:

• The mass of block B is $m_1=5.00 kg$.
• The mass of block A is $m_2=8.00 kg$.
• The static frictional coefficient between blocks A and B is ${\mathrm{μ}}_s=0.750$.

Tension is described as a force that acts on a body by virtue of its elastic nature. Moreover, tension is also considered as a pair of action and reaction forces.

The equation of the frictional force on the block B is expressed as:

$f={\mathrm{μ}}_s{m}_{1}g$

Here, f is the frictional force,${\mathrm{μ}}_s$ is the static frictional coefficient between the block A and B,$m_1$ is the mass of the block B and is the acceleration due to gravity.

Substitute the values in the above equation.

$$\begin{gathered} f=\left(0.750\right)\left(5.00kg\right)\left(9.8m/s^2\right) \\ =\left(3.75kg\right)\left(9.8m/s^2\right) \\ =36.75kg·m/s^2×\frac{1N}{1kg·m/s^2} \\ =36.75N \end{gathered}$$

The equation of the acceleration of the block B is expressed as:

$a=\frac{f}{m_1}$

Here, a is the acceleration of the block B.

Substitute the values in the above equation.

$$\begin{gathered} a=\frac{36.75N}{5.00kg} \\ =7.35N/kg \\ =7.35N/kg×\frac{1kg·m/s^2}{1N} \\ =7.35m/s^2 \end{gathered}$$

The equation of the mass of the block C is expressed as:

$$\begin{gathered} Mg-f=Ma+m_{2}a \\ {m}_{2}a+f=M\left(g-a\right) \\ \frac{m_{2}a+f}{g-a}=M \end{gathered}$$

Here, M is the mass of the block C.

Substitute the values in the above equation.

$$\begin{gathered} \mathrm{M}=\frac{\left(8.00\mathrm{kg}\right)\left(7.35\mathrm{m}/{\mathrm{s}}^2\right)+36.75\mathrm{N}}{\left(9.8\mathrm{m}/{\mathrm{s}}^2\right)-\left(7.35\mathrm{m}/{\mathrm{s}}^2\right)} \\ =\frac{\left(58.8\mathrm{kg}·\mathrm{m}/{\mathrm{s}}^2\right)+36.75\mathrm{N}×{\displaystyle \frac{1\mathrm{kg}·\mathrm{m}/{\mathrm{s}}^2}{1\mathrm{N}}}}{\left(2.45\mathrm{m}/{\mathrm{s}}^2\right)} \\ =\frac{\left(95.55\mathrm{kg}·\mathrm{m}/{\mathrm{s}}^2\right)}{\left(2.45\mathrm{m}/{\mathrm{s}}^2\right)} \\ =39\mathrm{kg} \end{gathered}$$

Thus, the largest mass the block C can have is 39 kg.