Molar mass of a protein from osmotic pressure
Osmotic pressure of a solute in water is given by the formula

$$\Pi = i\rm{MRT}\tag{1}$$

Where: 
$\Pi$ is the osmotic pressure 
$i$ is the Van't Hoff factor 
$\rm{M}$ is the molarity of the solute (mol/L) 
$\rm{R}$ is the universal gas constant 62.36 ($\rm{L}\space \rm{Torr}\space$ $\rm{K}^{−1}$ $\rm{mol}^{−1}$)
$\rm{T}$ is the absolute temperature ($^\circ\rm{K}$)

We'll assume $i =1$. 

Let's use $\rm{M_W}$ for the molecular weight of the protein. So the moles of the protein is equal to $\rm{g/M_W}$.

$$\dfrac{0.010\space\rm{g}/\rm{M_W}}{0.010\space\rm{L}}\times 62.36\space\rm{L}\space \rm{Torr}\space\rm{K}^{−1}\space\rm{mol}^{−1}\times293\space\rm{K}  = 52.2 \space \rm{Torr}\tag{2}$$

$$\rm{M_W} = \dfrac{0.010\times62.36\times293}{0.010\times52.2}\space\rm{g/mol}= 350\space\rm{g/mol}\tag{3} $$

Your mistake was believing the book answer. 


  If you need to check this sort of answer, then choose R with convenient units. It makes solving the problem much easier.