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A body having specific charge 8 $$\mu$$C g$$^{-1}$$ is resting on a frictionless plane at a distance 10 cm from the wall (as shown in the figure). It starts moving towards the wall when a uniform electric field of 100 V m$$^{-1}$$ is applied horizontally towards the wall. If the collision of the body with the wall is perfectly elastic, then the time period of the motion will be ___ s.
Correct Answer: 1
$$a = \frac{qE}{m} = \left(\frac{q}{m}\right)E = (8 \times 10^{-3}) \times 100 = 0.8\ \text{m/s}^2$$
Time taken to hit the wall from rest ($$s = \frac{1}{2}at^2$$):
$$t_1 = \sqrt{\frac{2d}{a}} = \sqrt{\frac{2(0.1)}{0.8}} = \sqrt{\frac{1}{4}} = 0.5\ \text{s}$$
Total time period ($$T = 2t_1$$): $$T = 2 \times 0.5 = 1\ \text{s}$$
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