Question

Two bar magnets of the same mass, same length and breadth but having magnetic moments M and 2M are joined together pole for pole and suspended by a string. The time period of assembly in a magnetic field of strength H is 3 seconds. If now the polarity of one of the magnets is reversed and combination is again made to oscillate in the same field, the time of oscillation is(a) √3 sec(b) 3√3 sec(c) 3 sec(d) 6 sec

Answer 1

answer : option (b) 3√3 sec

explanation : time period of oscillation of bar magnet in earth's magnetic field is given by, $T=2\pi\sqrt{\frac{I}{MH}}$

where, I is moment of inertia, M is net magnetic moment and H is horizontal component of earth's magnetic field.

case 1 : when bar magnets are placed in such a way that their similar poles are on same side .

then, net magnetic moment, $M_1=M+2M=3M$

so, time period,$T_1=2\pi\sqrt{\frac{I}{3MH}}$......(1)

case 2 : when bar magnets are placed in such a way that their similar poles are on opposite sides .

then, net magnetic moment, $M_2=2M−M=M$

so, time period, $T_2=2\pi\sqrt{\frac{I}{MH}}$......(2)

from equations (1) and (2),

$\frac{T_1}{T_2}=\frac{1}{\sqrt{3}}$

or, $T_2=\sqrt{3}T_1$

but we have given , $T_1=3sec$

so, $T_2=3\sqrt{3}sec$