Three masses m , 2 ~m and 3 ~m are moving in x - y plane with speed 3 u , 2 u and u respectively as shown in figure. The three masses collide at the same point at P and stick together. The velocity of resulting mass will be:

Step-by-step solution

From the law of conservation of momentum we know that, m ₁ u ₁+ m ₂ u ₂+ .= m ₁ v ₁+ m ₂ v ₂+ . Given m ₁= m , m ₂=2 ~m and m ₃=3 ~m and u ₁=3 u , u ₂=2 u and u ₃= u Let the velocity when they stick = v Then, according to question, aligned &m 3 u( i )+2 m 2 u (- i 60^ - j 60^ ) &+3 ~m u (- i 60^ + j 60^ ) &=( m +2 ~m +3 ~m ) v & 3 m u i -4 mu i 2 -4 mu ( 3 2 j )-3 mu i 2 &+3 m u ( 3 2 j )=6 ~m v & m u i - 3 2 m u i - 3 2 m j =6 ~m v & - 1 2 m u i - 3 2 m u j =6 ~m v & v = u 12 (- i - 3 j ) & aligned