Find the number of revolutions made by a proton in a cyclotron to attain one fourth of speed of light, if the maximum value of accelerating potential provided by the oscillator is 40 kV ? Take mass of the proton ` = 1.67 xx 10^(-27)` kg .

Explanation

To find the number of revolutions made by a proton in a cyclotron to attain one fourth of the speed of light, we can follow these steps:

### Step 1: Determine the speed of the proton
The speed \( v \) of the proton is given as one fourth of the speed of light \( c \):
\[ v = \frac{c}{4} = \frac{3 \times 10^8 \, \text{m/s}}{4} = 7.5 \times 10^7 \, \text{m/s} \]

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