Question

xample 13. A particle of mass 3 kg is moving under the action of a central force whose potential energ
is given by U (r) = 10 joule. For what energy and angular momentum will the orbit be a circle of radius
10 m? Calculate the time period of this motion.
3​

Answer 1

Answer:

Given data v=kr

3

d.w.r to 'r' m both sides

dv=3kr

2

Now ΔV=

m

Δu

⇒

m

dv

=dv=3kr

2

dr

[u=PE of mass m]

dr

du

=3kmr

2

F=

dr

−du

=∣F∣=3kmr

2

⇒2kmr

2

=

r

mv

2

(1) For circular motion F=F

centripetal

∴v=

3kr

3

for r=a∴v=

3ka

3

For circular motion

total energy ⇒E=K+U

=

2

1

mv

2

+mv

r

=

2

1

m(3ka

3

)+m(ka

3

)

E=

3

5

mka

3

Angular momentum = mvr=m

3ka

3

L=(ma

2

)

3ka

(2) Time for circular motion

T=

v

2πr

=

3ka

3

2π(a)

=

3ka

2π

thanks...