Explanation

(c) Energy of proton $= 2\ MeV$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = 2 \times 1.6 \times 10^{- 19} \times 10^{6}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ E = 3.2 \times 10^{- 13}\ J$
Magnetic field $(B) = 2.5\ T$
Mass of proton $(m) = 1.6 \times 10^{- 27}\ kg$
Energy of proton, $E = \frac{1}{2}\ mv^{2}$
$\therefore v = \sqrt{\frac{2E}{m}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ldots(i)$
Magnetic force on proton
$F = B\ qv\sin{90{^\circ}} = Bqv$
Substituting the value of $v$ from Eq. (i)
$F = Bq\ \sqrt{\frac{2E}{m}}$
$\ \ \ = 2.5 \times 1.6 \times 10^{- 19}\ \sqrt{\frac{2 \times 3.2 \times 10^{- 13}}{1.6 \times 10^{- 27}}}$
$\ \ \ = 8 \times 10^{- 12}\ N$