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Question

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


Solution

Let OX be the X-axis and point O (0, 0) be the origin of the system.

The mass of each brick is M.
The length of each brick is L.
Each brick is displaced with respect to another in contact by a distance L10.

∴ The X-coordinate of the centre of mass is given as,
Xcm= 17 mL10mL2+mL2+L10+..........+mL2Xcm= L2+L2+L10+L5+L2+3L10+L2+L5+L2+L10+L27      = 7L2+5L10+2L57 = 22L35

The X-coordinate of the centre of mass relative to the origin is 22L35.

Physics
HC Verma - I
Standard XI

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