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Question

A particle is constrained to move along x -axis with a velocity u along the positive x -axis. The acceleration a of the particle varies as a=bx, where b is a positive constant and x is the x-coordinate of the position of the particle. Then select the correct alternative(s)


A
The maximum displacement of the particle from the starting point is ub
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B
The particle will oscillate about the origin
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C
Velocity is maximum at the origin
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D
Given data is insufficient to determine the exact motion of the particle.
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Solution

The correct options are
A The maximum displacement of the particle from the starting point is ub
B The particle will oscillate about the origin
C Velocity is maximum at the origin

(A)

dvdt=bx=vdvdx
0uvdv=x0bxdx (at maximum dispacement upper limit of velocity = 0)
v220u=bx22x0

u22=bx22x=ub

(B)

F=m(bx)a=bx=ω2x
The particle will perform SHM

(C)
In case of SHM, velocity is maximum at the origin which is mean position of SHM.


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