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Q.

 In the figure below, the variation of potential energy of a particle of mass m = 2 kg is represented w.r.t its x-coordinate. The particle moves under the effect of the conservative force along the x-axis. Which of the following statements is incorrect about the particle?

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a

If it is released at x=2+Δ, where Δ0, then its maximum speed will be 5 m s-1 and it will perform oscillatory motion. 

b

 x = -5 and x = +5 are unstable equilibrium positions of the particle. 

c

 If initially x=10 and u=6i^,then it will cross x = 10. 

d

If it is released at the origin, it will move in negative x-axis
 

answer is D.

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Detailed Solution

If the particle is released at the origin, it will try to go in the direction of force. Here dU/dx is positive and hence force is negative; as a result, it will move towards negative x-axis. 

When the particle is released at x=2+Δ, it will reach the point of least possible potential energy (-15 J) where it will have maximum kinetic energy. 

12mvmax2=25vmax=5ms1

The particle will now perform oscillatory motion with x = 5 as mean position. 

 In (c), Ei=ui+ki=15+6=21J At x=10,Uf=20Kf=10

So the particle crosses x = 10. 

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