Question

A ball of mass M and speed of V collides head on with a ball of mass 2M and a speed of v/2, as

shown above. If the two balls stick together, their speed after the collision is

Answer 1

2/3V

Step-by-step explanation:

Given that a ball of mass M and speed V collides with another ball of mass 2M and velocity v/2 . After collision they stick together and we need to find their speed after collision . According to Law of Conservation of Momentum , The total momentum of the system before and after collision is constant .That is ;

`\sf\qquad\longrightarrow m_1u_1+m_2u_2=m_1v_1+m_2v_2\\`

`\sf\qquad\longrightarrow MV + 2M\bigg((V)/(2)\bigg) = (2M + M)(v)\\`

`\sf\qquad\longrightarrow MV +MV= 3Mv\\`

`\sf\qquad\longrightarrow 2MV = 3Mv\\`

`\sf\qquad\longrightarrow v =(2M)/(3M)V\\`

`\sf\qquad\longrightarrow \pink{ v_(after\ collision)=(2)/(3)V }`

Hence the velocity after the collision ia 2/3V .