Two girls Sita and Gita are skating towards each other on smooth ice along parallel lines as shown in figure. The distance between the lines is ℓ. The mass of two girls are m1 and m2 (m1 < m2) and their respective velocity are v1 and v2 (v2 > v1) . One of the girls holds a stick of length ℓ and negligible mass. When the girls pass each other, second girl grasps the stick and the girls move together, each of them on either side of the stick. Mark the correct statements -

Engineering

Physics

Center of Mass

Moment of Inertia

Angular Momentum and Conservation of Angular Momentum

Question

Two girls Sita and Gita are skating towards each other on smooth ice along parallel lines as shown in figure. The distance between the lines is ℓ. The mass of two girls are m₁ and m₂ (m₁ < m₂) and their respective velocity are v₁ and v₂ (v₂ > v₁) . One of the girls holds a stick of length ℓ and negligible mass. When the girls pass each other, second girl grasps the stick and the girls move together, each of them on either side of the stick. Mark the correct statements -

In the centre of mass reference frame of system both the girls have momentum of equal magnitude.

After the girl has grabbed the rod, system rotates in anticlock wise sense while centre of mass translates towards left.

Angular momentum of system about centre of mass increases.

If the girls start moving towards each other by pulling the stick, angular velocity of system will increase.

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|P₁ c| = |P₂ c| = µ V_rel
Angular momentum of system would remain conserved as there is no extermal torque.

v_cm = $\frac{m_{1} v_{1} - m_{2} v_{2}}{m_{1} + m_{2}}$ (m₂ v₂ > m₁ v₁)
∴ v_cm towards left. and would not change. Total initial $\vec{L}$ of system just before striking was in anticlock wise sense, so after striking also it would remain in the same sense