Question

50.
A particle is released from rest. in an electric field
E=5kV/mi. Initially particle is at (0, 0). When
displacement in y-direction is 84 cm, then find
displacement in x direction.
[g = 9.8 m/s2 and 9 = 10 uC/kg)
m
(1) 0.43 cm
(3) 8.6 cm
(2) 4.3 cm
(4) 0.86 cm​

Answer 1

answer : option (1) 0.43cm

explanation : first of all, find time taken to move 84cm along y-axis.

as we know, gravitational force acts along y-axis.

so, acceleration , a = 9.8 m/s²

displacement, s = 84cm = 0.84m

initial velocity of particle , u = 0

so, s = 1/2 gt²

or, 0.84 = 1/2 × 9.8 × t²

or, t² = 1.68/9.8 .....(1)

now acceleration along x-axis is due to electric field, E = 5kV/m = 5000V/m

then, acceleration, a = qE/m = (q/m)E

given, q/m = 10 uC/kg = 10^-5 C/Kg

so, a = 10^-5 × 5000 m/s² = 0.05 m/s²

now displacement, d = 1/2 at² [ as initial velocity is particle is zero ]

from equation (1),

= 1/2 × 0.05 × 1.68/9.8 m

= 0.0043 m or 0.43cm

= 0.43 cm

hence, option (1) is correct choice.