Calculate the velocity of the centre of mass of the system of particles shown in figure.
The correct option is B. 0.2 m/s
As we already know,
(Vx)com=∑mi(vi)x∑mi;(Vy)com=∑mi(vi)y∑mi and (Vz)com=∑mi(vi)z∑mi
As there is no particle in the given system where velocity has a component in Z direction, the component wise pictorial representation of all 5 particles is depicted as shown (assuming horizontal & vertical direction as x & y axes respectively).
Recall
cos 37∘ = 45
sin 37∘ = 35
Now ,
(Vx)COM = −1.5×45−(1×45×1.5)+(0.5×3)+(1×2×45)1+1.2+1.5+0.5+1
= 0.135 m/s
Similarly ,
(Vy)COM = −1.5×35+(1.2×0.4)+(1.5×35)+(2×1×35)5.2
(Vy)COM = 0.14 m/s
→Vnet = √(Vx)com2+(Vy)com2
= √(0.135)2+(0.14)2
= 0.2 m/s.