Problem 5: A proton is moving with a speed of 1 × 10⁷ m/s, passes through a 0.020 cm thick sheet of paper and emerges with a speed of 2.0 × 10⁶ ms^-1. Assuming uniform deceleration, find retardation and time taken to pass through the paper.

Solution

Given:                  v_i = 1 × 10⁷ ms^-1,                Thickness = distance = s = 0.02 cm = 0.02 × 10^-2 m,             

v_f = 2.0 × 10⁶ ms^-1

Find:                     Deceleration a and time t

To find the required quantities, we use equation of motion,

Put the values

This equation gives the deceleration of proton.

To find the time taken to pass through the paper, we use equation of motion v_f = v_i + at. Put values,