Comprehension # 5
One particle of mass `1 kg` is moving along positive x-axis with velocity `3 m//s`. Another particle of mass `2 kg` is moving along y-axis with `6 m//s`. At time `t = 0, 1 kg` mass is at `(3m, 0)` and `2 kg` at `(0, 9m), x - y` plane is the horizontal plane. (Surface is smooth for question 1 and rough for question 2 and 3)
If both the particles have the same value of coefficient of friction `mu = 0.2`. The centre of mass will stop at time `t =` ..........s :-

Options

A. `1.5`
B. `4.5`
C. `3.0`
D. `2.0`

Answer

C

Explanation

`vec(a)_(cm) = (m_(1)vec(a)_(1) + m_(2)vec(a)_(2))/(m_(1) + m_(2)) = (1 (-2hat(i)) + 2 (-2 hat(j)))/(1 + 2)`
`= -(2)/(3)(hat(i) + 2hat(j))m//s^(2)`
By using `vec(v)_(cm) = vec(u)_(cm) + vec(a)_(cm)t`, we get `t = 3s`