Question

Five identical thin square sheets of metal are joined at their edges to form a cubical box which is open at the top. Find the centre of mass of the box.

Answer 1

SOLUTION :--------->>>>>>>

مو | موه 2 3 2.

Centre of Mass of the square plate at the centre of the square

For 1234

M = (0, a/2, a/2)

For 5678

M = (a, a/2, a/2)

For 1769

M = (a/2, a/2, a)

For 3465

M = (a/2, 0, a/2)

For 2853

M = (a/2, a/2, 0)

For COM

X-axis

( M(0) + M(a) + M(a/2) + M(a/2) + M(a/2) ) / ( M + M + M + M + M )

( 5M(a/2) ) / ( 5M ) =  a/2

Y-axis

( M(a/2) + M(a/2) + M(a/2) + M(0) + M(a/2) ) / (5M)

( 2M(a) ) / ( 5M(a) )  = 2a/5

Z-axis

( M(a/2) + M(a/2) + M(a) + M(a/2) + M(0) ) / ( 5M )

( 5M(a/2) ) / ( 5M )  = a/2

COM from bottom corner

COM =  
+ + 4/

=  

(a/2)2 + (2a/5)2 + (a/5)2

  =
{V66) a/10
ANS

THANKS

+ + 4/

(a/2)2 + (2a/5)2 + (a/5)2

{V66) a/10