Question

At a certain place a magnet makes 30 oscillations per minute. At another place where the magnetic field is double, its time period will be

• A. 4 sec
• B. 2 sec
• C.
• D. $\sqrt { 2 } \mathrm { sec }$

Answer 1

Answer: (D)

$\sqrt { 2 } \mathrm { sec }$

Answer 2

$T = 2 \pi \sqrt { \frac { I } { M B _ { H } } } ; \therefore \frac { T _ { 1 } } { T _ { 2 } } = \sqrt { \frac { \left( B _ { H } \right) _ { 2 } } { \left( B _ { H } \right) _ { 1 } } } \Rightarrow T _ { 2 } = T _ { 1 } \sqrt { \frac { \left( B _ { H } \right) _ { 1 } } { \left( B _ { H } \right) _ { 2 } } }$

Here n₁=30 oscillation /min $= \frac { 1 } { 2 }$oscillation/sec

$\therefore T _ { 1 } = \frac { 1 } { n _ { 1 } } = 2 \mathrm { sec }$

$\therefore T _ { 2 } = 2 \sqrt { \frac { B _ { H } } { 2 B _ { H } } } = 2 \times \frac { 1 } { \sqrt { 2 } } = \sqrt { 2 } \mathrm { sec }$