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A three$-$point bending test is performed on a glass specimen having a rectangular cross section of height $5\mathrm{.}5$ mm and width $12\mathrm{.}0$ mm ; the distance between support points is $41$ mm $.$

$($a$)$ Calculate the flexural strength $($in MPa$)$ if the load at fracture is $300$ N $.$

${}_{fs}=$

$$

MPa

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

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

where $E$ is the modulus of elasticity and I the cross$-$sectional moment of inertia. Calculate $y$ of $252$ N $.$ Assume that the elastic modulus for the glass is $70$ GPa $.$

$y=$

$$

$m$

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