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Solve the following :

Question:

In a TV picture tube electrons are ejected from the cathode with negligible speed and reach a velocity of $5 \times 10^{6} \mathrm{~m} / \mathrm{s}$ in travelling one centimeter. Assuming straight line motion, find the constant force exerted on the electron. The mass of the electron is $9.1 \times 10^{-31} \mathrm{~kg}$.

Solution:

$u=0$ (negligible)

$v=5 \times 10^{6} \mathrm{~m} / \mathrm{s}$

$v^{2}=u^{2}+2 a s$

$\left(5 \times 10^{6}\right)^{2}=(0)^{2}+2 a\left(1 \times 10^{-2}\right)$

$a=12.5 \times 10^{14} \mathrm{~m} / \mathrm{s}^{2}$

$F=m a=9.1 \times 10^{-31} \times 12.5 \times 10^{14}$

$=1.138 \times 10^{15} \mathrm{~N}$