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Question

As shown in figure, a particle of mass 2 kg is attached to a bead. The bead can slide on a smooth straight wire. Length of the string which connect the particle and the bead is l. Initially, the particle is held in contact with the wire with the string taut as shown in figure, and then it is let to fall. If the bead has a mass 4 kg, then, when the string makes an angle θ=60∘ with the wire, find the distance it slides upto this instant.

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Solution

The correct option is **B** l6 towards right

When string make an angle 60∘ with the wire:

Let the bead travel x distance as shown above.

Then, the distance covered by the 2 kg particle in x direction is =[−(l−lcosθ)+x]

and the distance covered by the bead =x (towards right)

As we know, there is no external force acting on the system. So, xcom will not change. It will be zero.

xcom=m1x1+m2x2m1+m2=0

(Assuming motion towards right to be positive.)

xcom=4×(x)+2(lcos60∘−l+x)4+2

⇒4x−2l+2lcos60∘+2x=0

⇒6x−l=0

⇒x=l6

+ve sign means the bead will move towards right.

When string make an angle 60∘ with the wire:

Let the bead travel x distance as shown above.

Then, the distance covered by the 2 kg particle in x direction is =[−(l−lcosθ)+x]

and the distance covered by the bead =x (towards right)

As we know, there is no external force acting on the system. So, xcom will not change. It will be zero.

xcom=m1x1+m2x2m1+m2=0

(Assuming motion towards right to be positive.)

xcom=4×(x)+2(lcos60∘−l+x)4+2

⇒4x−2l+2lcos60∘+2x=0

⇒6x−l=0

⇒x=l6

+ve sign means the bead will move towards right.

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