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119. Problem 15.47 (RHK) A physical pendulum consists of a meter stick that is pivoted at a small hole drilled through the stick a distance x from the 50.0-cm mark. The period of oscillation is observed to be 2.50 s. We have to find the distance x. |
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Solution: Click For PDF Version Let the mass of the meter stick be m. We denote its
length, which is 1.0 m, by L. The rotational inertia of the stick about
the axis passing through its centre of mass is
Period of the physical pendulum is given by the expression
Substituting L = 1.0 m and T= 2.50 s, we have the quadratic equation
Roots of this quadratic equation are
As we are considering oscillations of a meter rod, the physical solution is
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Therefore, its rotational inertia about the axis passing through the pivot,
which is at a distance x from the centre of the meter stick, will be
