Two small magnets have their masses and lengths in the ratio 1 : 2. the maximum torques experienced by them in a uniform magnetic field are the same. For small oscillations, the ratio of their time periods is

Options

A. `(1)/(2sqrt(2))`
B. `(1)/(sqrt(2))`
C. `((1)/(2))`
D. `2sqrt(2)`

Answer

A

Explanation

Mass of first magnet `=m`
Mass of second magnet =2m
Time - period of oscillation of magnet,
`T=2pi sqrt((I)/(M B_H))`
`(T_1)/(T_2)=sqrt(((I_1)/(M_1)xx(M_2)/(I_2))`
`I=(mL^2)/(3)rArr I_(1)=(Ml^2)/(3)`
`I_(2)=(2m(2L)^2)/(3)`
Maximum torques experienced by the magnets are same.
`M_1.B_4=M_2B_4 rArr M_1 =M_2`
`(T_1)/(T_2)=sqrt((1)/(8))=(1)/(2sqrt(2))`.