Question

A particle, which is constrained to move along the x-axis, is subjected to a force in the same direction whic
varies with the distance x of the particle x of the particle from the origin as f(x) =-kx+ ax? here anda
positive constants. forx20, the functional form of the potential energy u (x) of the particle is
[jee (scr.'2002]

Answer 1

Answer:

GivenForceF(x)=−kx+ax

3

WeknowthatU(x)=−∫

0

x

F(x)dx=

2

kx

2

−

4

ax

4

ForU(x)=0andx≥0wehavex=0andx=

a

2k

dx

d(U(x))

=kx−ax

3

=x(k−ax

2

)

Now,

dx

d(U(x))

=0⇒x=0,

a

k

Explanation:

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