A three$-$point bend test is performed on a block of silicon carbide that is $10$ cm long, $1\mathrm{.}5$ cm wide, and $0\mathrm{.}6$ cm thick and is resting on two supports $7\mathrm{.}5$ cm apart. The sample breaks when a deflection of $0\mathrm{.}09$ mm is recorded. The flexural modulus for silicon carbide is $480$ GPa $.$ Assume that no plastic deformation occurs. Calculate

$($a$)$ the force that caused the fracture;

$($b$)$ the flexural strength.