The period of oscillations of a magnetic needle in a magnetic field is 1.0 sec. If the length of the needle is halved by cutting it, the time perood will be

Options

A. `1.0 sec`
B. `0.5 sec`
C. `0.25 sec`
D. `2.0 sec`

Answer

B

Explanation

`T=2pisqrt(I/(MB))=2pisqrt((wl^(2)//12)/("Pole strength" xx2lxxB))`
`:.T propsqrt(Wl)`
`:.T_(2)/T_(2)=sqrt(w_(2)/w_(1)xxl_(2)/l_(1))=sqrt((w_(1)//2)/w_(1)xx(l_(1)//2)/l_(1))=1/2`
`impliesT_(2)=T_(1)/2=0.5s`