Consider a physical pendulum and a simple pendulum both of length L . The physical pendulum is a thin rigid and uniform rod hinged to the ceiling so that it is free to swing back and forth about its one end. Now for a small oscillation, find the ratio of time periods of the physical pendulum and the simple pendulum:

Question

Consider a physical pendulum and a simple pendulum both of length L . The physical pendulum is a thin rigid and uniform rod hinged to the ceiling so that it is free to swing back and forth about its one end. Now for a small oscillation, find the ratio of time periods of the physical pendulum and the simple pendulum: (A) √(3/2) (B) √(2/3) (C) (2/3) (D) (3/2)

Tardigrade Admin · Accepted Answer

In case of rod we will consider it a compound pendulum. the time period of physical pendulum will be TA=2π √(Io/m g l) Io= moment of inertia of rod l= length of rod. TA=2π √((m l2/3)/(m g l)2)=2π √(2 l/3 g) .......(1) for simple pendulum and Tn=2π √(l/g)⇒ (TA/Tb)=√(2/3) .......(2)

$\frac{3}{2}$

$\frac{2}{3}$

$\frac{2}{3}$

$\frac{3}{2}$

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$\frac{3}{2}$

$\frac{2}{3}$

$\frac{2}{3}$

$\frac{3}{2}$