Question

Four bodies of masses 1 kg, 2 kg, 3 kg and 4 kg are at the vertices of a
rectangle of sides a and b. If a =
1 mand b - 2 m, find the location of the
centre of mass. Assume t
hat, 1 kg mass is at the origin of the system, 2 kg
body is situated along the positive axis and 4 kg along the y axis.)​

Answer 1

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Four particles of masses 1kg, 2kg, 3kg and 4kg are placed at the four vertices A, B, C and D of a square of side 1m. Find the position of centre of mass of the particles.

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Text Solution

Answer :

C

Solution :

Assuming D as the origin, DC as x-axis and DA as y-axis, we have

m1=1kg,(x1,y1)=(0,1m)

m2=2kg,(x2,y2)=(1m,1m)

m3=3kg,(x3,y3)=(1m,0)

and m4=4kg,(x4,y4)=(0,0)

Coordinates of their COM are

xCOM=m1x1+m2x2+m3x3+m4x4 / m1+m2+m3+m4

= (1)(0)+2(1)+3(1)+4(0) / 1+2+3+4

= 5 / 10= 1/2 m= 0.5m

Similarly,

yCOM=m1y1+m2y2+m3y3+m4y4/m1+m2+m3+m4

11+2(1)+3(0)+4(0)1+2+3+4

=3/10m=0.3m