KVPY2010PhysicsCenter of Mass, Momentum and Collision
Two masses m ₁ and m ₂ are connected by a massless spring of spring constant k and unstreched length . The masses are placed on a frictionless straight channel - which we consider our x -axis. They are initially at rest at x =0 and x = , respectively. At t =0 , a velocity of v ₀ is suddenly imparted to the first particle. At a later time to, the centre of mass of the two masses is at-
Options
- Ax = m ₂ m ₁+ m ₂
- Bx = m ₁ m ₁+ m ₂ + m ₂ v ₀ t m ₁+ m ₂
- Cx = m ₂ m ₁+ m ₂ + m ₂ v ₀ t m ₁+ m ₂
- Dx = m ₂ m ₁+ m ₂ + m ₁ v ₀ t m ₁+ m ₂
Correct answer
D. x = m ₂ m ₁+ m ₂ + m ₁ v ₀ t m ₁+ m ₂
Step-by-step solution
array l v _ COM = m ₁ v ₀+0 ~m ₁+ m ₂ , x _ iCOM = m ₁(0)+ m ₂( ) m ₁+ m ₂ also x _ COM = x _ COM + v _ Com t x _ COM = ( m ₂ m ₁+ m ₂ )+ m ₁ v ₀ t m ₁+ m ₂ array