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 (3 m,0) and 2 kg at (0,9 m). x-y plane is the horizontal plane. (surface is smooth for question 15 and rough for questions 16 and 17).
If both the particle 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`