A three$-$point bending test is performed on a glass specimen having a rectangular cross section of height $4\mathrm{.}4$ mm and width $10\mathrm{.}6$ mm ; the distance between support points is $47$ mm $.$

$($a$)$ Calculate the flexural strength $($in MPa $)$ if the load at fracture is $287$ N $.$

${}_{f_s}=$

$.$ 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 $257$ N $.$ Assume that the elastic modulus for the glass is $63$ GPa $.$

$y=,m$