A short bar magnet having magnetic moment 4 `Am^(2),` placed in a vibrating magnetometer, vibrates with a time period of 8 s. Another short bar magnet having a magnetic moment `8Am^(2)` vibrates with a time period of 6 s. If the moment of intertia of the second magnet is `9xx10^(-2)kg-m^(2)`, the moment of intertia of the first magnet is (assume that both magnets are kept in the same uniform magnetic induction field.)

Options

A. `9xx10^(-2)kg-m^(2)`
B. `8xx10^(-2)kg-m^(2)`
C. `5.33xx10^(-2)kg-m^(2)`
D. `12.2xx10^(-2)kg-m^(2)`

Answer

B

Explanation

Time period of vibrating bar magnet,
`T=2pisqrt((I)/(MB_(H)))`
`T_(1)=8s,T_(2)=6s,I_(2)=90xx10^(-2),M_(1)=4,M_(2)=8` given
`(T_(1))/(T_(2))=sqrt((I_(1))/(I_(2))xx(M_(2))/(M_(1))`
`implies8/6=sqrt((I_(1))/(9xx10^(-2))xx(8)/(4)`
`(4/3)^(2)=(I)/(9xx10^(-2))xx2`
`impliesI_(1)=(16xx9xx10^(-2))/(9xx2)`
`=8xx10^(-2)kg-m^(2)`