Question

Magnets A and B are geometrically similar but the magnetic moment of A is twice that of B. If T₁ and T₂ be the time periods of the oscillation when their like poles and unlike poles are kept together respectively, then $\frac { T _ { 1 } } { T _ { 2 } }$will be

• A. $\frac { 1 } { 3 }$
• B. $\frac { 1 } { 2 }$
• C. $\frac { 1 } { \sqrt { 3 } }$
• D. $\sqrt { 3 }$

Answer 1

Answer: (C)

$\frac { 1 } { \sqrt { 3 } }$

Answer 2

$T _ { S u m } = 2 \pi \sqrt { \frac { \left( I _ { 1 } + I _ { 2 } \right) } { \left( M _ { 1 } + M _ { 2 } \right) B _ { H } } }$

$T _ { \text {diff } } = 2 \pi \sqrt { \frac { I _ { 1 } + I _ { 2 } } { \left( M _ { 1 } - M _ { 2 } \right) B _ { H } } }$

$\Rightarrow \frac { T _ { s } } { T _ { d } } = \frac { T _ { 1 } } { T _ { 2 } } = \sqrt { \frac { M _ { 1 } - M _ { 2 } } { M _ { 1 } + M _ { 2 } } } = \sqrt { \frac { 2 M - M } { 2 M + M } } = \frac { 1 } { \sqrt { 3 } }$