Question

A magnet of magnetic moment M oscillating freely in earth's horizontal magnetic field makes n oscillations per minute. If the magnetic moment is quadrupled and the earth's field is doubled, the number of oscillations made per minute would be

• A. $\frac { n } { 2 \sqrt { 2 } }$
• B. $\frac { n } { \sqrt { 2 } }$
• C. $2 \sqrt { 2 } n$
• D. $\sqrt { 2 } n$

Answer 1

Answer: (C)

$2 \sqrt { 2 } n$

Answer 2

No. of oscillation per minute

$= \frac { 1 } { 2 \pi } \sqrt { \frac { M B _ { H } } { I } }$

$\begin{aligned} \Rightarrow n \propto \sqrt { M B _ { H } } ; M & \rightarrow 4 \text { times } \\ B _ { H } & \rightarrow 2 \text { times } \end{aligned}$

So $v \rightarrow \sqrt { 8 }$ times i.e. $v ^ { \prime } = \sqrt { 8 } v = 2 \sqrt { 2 } n$