Question

A cyclotron accelerates a proton to a final speed of $3\times {10}^{7}m{s}^{-1}$, which is initially at rest. The work done on the proton in mega electron volts, by the electric field of the cyclotron is:

(Mass of the proton is $1.6\times {10}^{-27}kg$)

• A. $0.45$
• B. $4.5$
• C. $45$
• D. $450$

Answer 1

Answer: (B)

$4.5$

$W.D=\Delta K.E=\frac{1}{2}m{v}^2$

As speed of proton is aprrox. $c/10$, we can get away with ignoring relativistic effect.

$W=\frac{1}{2}\times 1.6\times {10}^{-27}\times (3\times {10}^7{)}^2$

Work done by cyclotron $=4.5Mev$