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The center of mass is located at position i EX.5.4. Locate the center of mass of a uniform rod of mass M and length |
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Answer» Solution :Consider a uniform ROD of mass M and length / whose one END coincides with the origin as shown in Figure. The rod is kept along the x AXIS. To find the CENTER of mass of this rod, we choose an infinitesimally small mass dm of elemental length dr at a DISTANCE from the origin `lambda`is the linear mass density (ie, mass per unit length) of the rod. `lambda=(M)/(l)` The mass of small element (dm) is `dm, (M)/(l)dx` Now, we can write the center of mass equation for this mass distribution as, `X_(CM)=(int x dxm)/( int dm)` `X_(CM)=( overset(1) underset(0) intx((M)/(l)dx))/(M)=(1)/(l)overset(1) underset(0) intxdx=(1)/(l)[(x^(2))/(2)]_(0)^(l)=(1)/(l)=((t^(2))/(2))` `X_(CM)=(l)/(2)` As the `(l)/(2)` position is the geometric center of the rod, it is concluded that the center of mass 
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