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Question

Calculate the velocity of the centre of mass of the system of particles shown in figure.


A

0.4 m/s

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B

0.2 m/s

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C

0.8 m/s

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D

1 m/s

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Solution

The correct option is B. 0.2 m/s


As we already know,
(Vx)com=mi(vi)xmi;(Vy)com=mi(vi)ymi and (Vz)com=mi(vi)zmi
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.


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