Question

(iv) Prove that under the influence of a central force the motion of a particle is always ` confined to a plane.`​

Answer 1

Answer:

Yes this is right I think

Answer 2

It is true that under the influence of a central force the motion of a particle is always confined to plane.

Solution,

• A central force is always directed towards or away from a fixed point, depending on where the force is applied in relation to the fixed point. The angular momentum of a particle moving under the central force is always conserved. As a result, the motion of a particle subjected to the central force is always restricted to a plane.

We know that a central force can exert no torque on an object:

τ=r×F

=F(r)(r×r^)=0

As a result, under the action of a central force , angular momentum conserved.

So for momentum we know,

  r . L=r.(r×p)=0

So,

v . L=v.(r×mv)=0

Both vector r and v are in a plane which is perpendicular to L.As we know momentum L is conserved then r and v must confined to the plane perpendicular to L through the origin.