A particle of mass m = 1 kg lying on x-axis experiences a force given by law
= x (3x – 2) 
Newton,
where x is the x-coordinate of the particle in meters.
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
x = 0 and x = 
m
The particle is in stable equilibrium at x = 0 meter and unstable equilibrium at x = 
meter
v = 
m/s
Sol. The particle is at equilibrium when F = 0
⇒ x (3x – 2) = 0
⇒ x = 0 and x = 
m
The particle is in stable equilibrium at x = 0 meter and unstable equilibrium at x = 
meter
Since at x = 0
⇒ 
and at x = 
m 
⇒ 
The minimum speed imparted to the particle should be such that it just reaches x = 
from there on it shall automatically reach x = 0
mv 2 = – 
= – 
= 
or k v = 
m/s
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