JEE MAIN - Physics (2021 - 20th July Morning Shift - No. 20)
A body having specific charge 8 $$\mu$$C/g 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 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.
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Answer
1
Explanation
Given,
q = 8$$\mu$$C/g = 8 $$\times$$ 10$$-$$6 C/g = 8 $$\times$$ 10$$-$$3 C/kg
s = 10 cm = 0.1 m $$\Rightarrow$$ E = 100 V/m
We know that, acceleration, a = $${{force(F)} \over {mass(m)}}$$
$$\Rightarrow$$ a = $${{qE} \over m}$$ [$$\because$$ F = qE]
= $${{8 \times {{10}^{ - 6}} \times 100} \over {{{10}^{ - 3}}}}$$ = 0.8 ms$$-$$2
As per question, when electric field is switched on, the body strikes to the wall and then returns back.
For one oscillation,
s = ut + $${1 \over 2}$$ at2
$$\Rightarrow$$ 0.1 = $${1 \over 2}$$ $$\times$$ 0.8 t2 [$$\because$$ u = 0]
$$\Rightarrow$$ 0.2 = 0.8 t2
$$\Rightarrow$$ $${2 \over 8}$$ = t2 $$\Rightarrow$$ t2 = $${1 \over 4}$$ $$\Rightarrow$$ t = $${1 \over 2}$$
$$\therefore$$ Time period = 2 $$\times$$ $${1 \over 2}$$ = 1 s
Therefore, if the collision of the body is perfectly elastic, the time period of motion will be 1s.
q = 8$$\mu$$C/g = 8 $$\times$$ 10$$-$$6 C/g = 8 $$\times$$ 10$$-$$3 C/kg
s = 10 cm = 0.1 m $$\Rightarrow$$ E = 100 V/m
We know that, acceleration, a = $${{force(F)} \over {mass(m)}}$$
$$\Rightarrow$$ a = $${{qE} \over m}$$ [$$\because$$ F = qE]
= $${{8 \times {{10}^{ - 6}} \times 100} \over {{{10}^{ - 3}}}}$$ = 0.8 ms$$-$$2
As per question, when electric field is switched on, the body strikes to the wall and then returns back.
For one oscillation,
s = ut + $${1 \over 2}$$ at2
$$\Rightarrow$$ 0.1 = $${1 \over 2}$$ $$\times$$ 0.8 t2 [$$\because$$ u = 0]
$$\Rightarrow$$ 0.2 = 0.8 t2
$$\Rightarrow$$ $${2 \over 8}$$ = t2 $$\Rightarrow$$ t2 = $${1 \over 4}$$ $$\Rightarrow$$ t = $${1 \over 2}$$
$$\therefore$$ Time period = 2 $$\times$$ $${1 \over 2}$$ = 1 s
Therefore, if the collision of the body is perfectly elastic, the time period of motion will be 1s.
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