Three interacting particles of masses `100g, 200g` and `400g` each hace a velocity of `20 m//s` magnitude along the positive direction of x-axis, y-axis and z-axis. Due to force of interaction the third particle stops moving. The velocity of the second particle is `(10hat(j) + 5hat(k))`. What is the velocity of the first particle ?

Options

A. `20hat(i) + 20hat(j) + 70hat(k)`
B. `10hat(i) + 20hat(j) + 8hat(k)`
C. `30hat(i) + 10hat(j) + 7hat(k)`
D. `15hat(i) + 5hat(j) + 60hat(k)`

Answer

(A)

Explanation

Initial momentum `= m_(1) vec(v)_(1) + m_(2)vec(v)_(2) + m_(3)vec(v)_(3) = 2hat(i) + 4hat(j) + 8hat(k)`
When the third particle stops the final momentum `= m_(1)vec(v)_(1) + m_(2)vec(v)_(1) + m_(2)vec(v)_(2) + m_(3)vec(v)_(3) = 0.1vec(v)_(1) + 0.2(10hat(j) + 5hat(k)) + 0`
By principle of conservation of momentum `0.1 vec(v)_(1) + 2hat(j) + hat(k) = 2hat(i) + 4hat(j) + 8hat(k), vec(v)_(1) = 20hat(i) + 20hat(j) + 70hat(k)`