1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# Four particles of masses m1=2m, m2=4m, m3=m and m4 respectively are placed at the four corners of a square. What should be the value of mass m4 so that the centre of mass of the system of particles lies at the centre of square?

A
m
No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
B
2m
No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
C
4m
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
6m
No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
Open in App
Solution

## The correct option is C 4m Considering a square with side a and assigning origin (0,0) at mass m1 . The x and y coordinates of all masses can be written as :m1=2m,(0,0)m2=4m,(a,0)m3=m,(a,a)m4=m4,(0,a) ∵ COM of system of particles should be at the centre of the square. Hence coordinates of COM is represented by (xCOM, yCOM)=(a2,a2)....(i) Applying the formula and equating the x and y coordinates of COM from Eq. (i) xCOM=m1x1+m2x2+m3x3+m4x4m1+m2+m3+m4 ⇒a2=0+4ma+ma+02m+4m+m+m4=5ma(7m+m4)...(ii) Simillarly, yCOM=m1y1+m2y2+m3y3+m4y4m1+m2+m3+m4 ⇒a2=0+0+ma+m4a7m+m4=(m+m4)a7m+m4.....(iii) Equating Eq. (ii) & (iii): 5ma=(m+m4)a ⇒m4=5m−m=4m ∴m4=4m

Suggest Corrections
22
Join BYJU'S Learning Program
Related Videos
Just an Average Point?
PHYSICS
Watch in App
Join BYJU'S Learning Program