Two equal -ve charges -q are fixed at the point (O, a) and (O, a) on the y-axis. A positive charge Q is released from rest at the point (2a, 0) on the x-axis. The charge will :

execute SHM about the origin

move to the origin and remain at rest

move to infinity

execute oscillatory but not SHM

Solution

execute oscillatory but not SHM

Component of force on charge +Q at P, along the x-axis,

$F_{x} = \frac{2 Qq}{4 {πε}_{o} (a^{2} + x^{2})} cosθ = \frac{2 Qq}{4 {πε}_{o} (a^{2} + x^{2})} \times \frac{x}{\sqrt{a^{2} + x^{2}}} F_{x} = \frac{2 Qqx}{4 {πε}_{o} {(a^{2} + x^{2})}^{\frac{3}{2}}}$

Which is directly proportional to x. So, motion is an oscillatory but not SHM.

Some More Questions From Oscillations Chapter

The displacement of an object attached to a spring and executing simple harmonic motion is given by x = 2 × 10^-2 cos πt metres. The time at which the maximum speed first occurs

A particle of mass m executes simple harmonic motion with amplitude ‘a’ and frequency ‘ν’. The average kinetic energy during its motion from the position of equilibrium to the end is

A coin is placed on a horizontal platform which undergoes vertical simple harmonic motion of angular frequency ω. The amplitude of oscillation is gradually increased. The coin will leave contact with the platform for the first time

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Oscillations

Two equal -ve charges -q are fixed at the point (O, a) and (O, a) on the y-axis. A positive charge Q is released from rest at the point (2a, 0) on the x-axis. The charge will :

execute SHM about the origin

move to the origin and remain at rest

move to infinity

execute oscillatory but not SHM

Some More Questions From Oscillations Chapter

The displacement of an object attached to a spring and executing simple harmonic motion is given by x = 2 × 10^-2 cos πt metres. The time at which the maximum speed first occurs

A particle of mass m executes simple harmonic motion with amplitude ‘a’ and frequency ‘ν’. The average kinetic energy during its motion from the position of equilibrium to the end is

A coin is placed on a horizontal platform which undergoes vertical simple harmonic motion of angular frequency ω. The amplitude of oscillation is gradually increased. The coin will leave contact with the platform for the first time

The function sin²(ωt) represents

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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Loaction

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Oscillations

Two equal -ve charges -q are fixed at the point (O, a) and (O, a) on the y-axis. A positive charge Q is released from rest at the point (2a, 0) on the x-axis. The charge will : execute SHM about the origin move to the origin and remain at rest move to infinity execute oscillatory but not SHM

Some More Questions From Oscillations Chapter

The displacement of an object attached to a spring and executing simple harmonic motion is given by x = 2 × 10-2 cos πt metres. The time at which the maximum speed first occurs

A particle of mass m executes simple harmonic motion with amplitude ‘a’ and frequency ‘ν’. The average kinetic energy during its motion from the position of equilibrium to the end is

A coin is placed on a horizontal platform which undergoes vertical simple harmonic motion of angular frequency ω. The amplitude of oscillation is gradually increased. The coin will leave contact with the platform for the first time

The function sin2(ωt) represents

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Two equal -ve charges -q are fixed at the point (O, a) and (O, a) on the y-axis. A positive charge Q is released from rest at the point (2a, 0) on the x-axis. The charge will :

execute SHM about the origin

move to the origin and remain at rest

move to infinity

execute oscillatory but not SHM

The displacement of an object attached to a spring and executing simple harmonic motion is given by x = 2 × 10^-2 cos πt metres. The time at which the maximum speed first occurs

The function sin²(ωt) represents