Question

A body having specific charge 8 µC/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 toward the wall. If the collision of the body with the wall is perfectly elastic, then the time period of the motion will be ______ s.

Options

• 1

• 5

• 4

• 2

Answer 1

A body having specific charge 8 µC/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 toward the wall. If the collision of the body with the wall is perfectly elastic, then the time period of the motion will be 1 s.

Explanation:

Electric force, F = qE

ma = qE

`a = (qE)/m`

Apply the second equation of motion,

`d = ut + 1/2at^2` [∵ u = 0 m/s]

`d = 1/2 at^2 = 1/2[(qE)/m]t^2`

t = `sqrt((2d)/((qE)/m)) = sqrt((2 xx 0.1)/(8 xx 10^-3(100)))`

= `sqrt(2000/8000) = 1/2`

It will take the same amount of time to return to its original position.

Time period (T) = `2(1/2)` = 1s.