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Q.

Two collars, A of mass 2m and B of mass 3m are connected by a massless rod with pinjoints so that they are constrained to move along the fixed perpendicular rods on horizontal plane, as shown in the accompanying figure. Another collar C of mass m hits A with speed $' v'$ and sticks to it. There is no friction between collars and rods.

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a

The speed of collar B just after the impact is $\frac{v \sin 2 α}{6}$

b

The speed of collar B just after the impact is $\frac{v \cos 2 α}{3}$

c

The speed of collar C just after the impact is $\frac{v \cos^{2} α}{3}$

d

The speed of collar A just after the impact is $\frac{v \sin^{2} α}{3}$

answer is B, C.

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Detailed Solution

Let the impulse due to the rod be T.
$m v - T \cos α = 3 m v_{1}$ where, $v_{1}$ is the speed of $(A + C)$ just after the collision.
$T \sin α = 3 m V_{2}$ where $V_{2}$ is the speed of B from the inextensibility of rod AB
$V_{1} \cos α = V_{2} \sin α$

Thus, $V_{1} = \frac{v \sin^{2} α}{3} & V_{2} = \frac{v \sin 2 α}{6}$

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Two collars, A of mass 2m and B of mass 3m are connected by a massless rod with pinjoints so that they are constrained to move along the fixed perpendicular rods on horizontal plane, as shown in the accompanying figure. Another collar C of mass m hits A with speed 'v' and sticks to it. There is no friction between collars and rods.