A three$-$point bending test is performed on a glass specimen having a rectangular cross section of height $5\mathrm{.}0$ mm and width $11\mathrm{.}8$ mm ; the distance between support points is $49$ mm $.$

$($a$)$ Calculate the flexural strength $($in MPa $)$ if the load at fracture is $281$ N $.$

${}_{fs}=$

MPa

$($b$)$ The point of maximum deflection $y$ occurs at the center of the specimen and is described by the expression

$y=\frac{F{L}^3}{48EI}$

where E is the modulus of elasticity and I the cross$-$sectional moment of inertia. Calculate $y$ of $269$ N $.$ Assume that the elastic modulus for the glass is $64$ GPa $.$

$y=$

$$

m