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Question

A uniform rod of length 10 m is placed along x axis as shown in figure. The distance of the centre of mass of the rod from the origin is


  1. 20 m
  2. 5 m
  3. 15 m
  4. 25 m


Solution

The correct option is C 15 m
Let the mass of uniform rod be M.
Mass per unit length of the rod (λ)=ML= constant           
( Rod is uniform)
Let dm be the mass of elemental length dx at a distance x from the origin.
dm=(ML)dx=(M10)dx
To find position of centre of mass,
xCOM=xdmdm=2010x×[M10dx]2010M10dx
=2010xdx2010dx=110[x22]2010
=110((20)2(10)22)
=15 m

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