Question

Seven homogeneous bricks, each of length L, are arranged as shown in figure (9-E2). Each brick is displaced with respect to the one in contact by L/10. Find the x-coordinate of the of the center of mass relative to the origin shown.

Answer 1

Thanks for asking the question!

ANSWER::

See figure for better understanding.

Take 'O' (0,0) be origin of system.

Given:-
Each brick has mass 'M' and length 'L'.
Each brick is displaced with respect to one in contact by "L/10"

X coordinate of the centre of the mass::

X cm = [m(L/2) + m(L/2 + L/10) + m(L/2 + 2L/10) + m(L/2 + 3L/10) + m(L/2 + 3L/10 - L/10) + m(L/2 + L/10) + m(L/2)] / 7m

= [(L/2) + (L/2 + L/10) + (L/2 + 2L/10) + (L/2 + 3L/10) + (L/2 + 3L/10 - L/10) + (L/2 + L/10) + (L/2)] / 7

= [7L/2 + 5L/10 + 2L/5 ] / 7

= [35L + 5L + 4L] / 10 x 7

= 44L/70

= 22L/35

Hope it helps!

Answer 2

Answer:

22L/35 is the x-coordinate of the center of mass relative to the origin.