A rod AB of length L is hung from two identical wires 1 and 2. A block of mass m is hung at point O of the rod as shown in fig. The value of x so that a tuning fork excites the fundamental mode in wire 1 and the second harmonic in wire 2 is
The correct option is C. L5
Let T1 and T2 be the tensions in wires 1 and 2 respectively. Let m be the mass per unit length of each wire and l be the length of each wire.
Given
l2l√T1m=22l√T2m
which gives T1T2=4
For rotational equilibrium of the rod about O, we have
T1×AO=T2×BO or T1×x=T2(L−x)
4=(L−x)x
which gives x=L5.
Hence the correct choice is (a).