Question

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 period will be

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

Answer 1

Answer: (B)

0.5 sec

Answer 2

$\therefore T \propto \sqrt { W l }$

$\therefore \frac { T _ { 2 } } { T _ { 1 } } = \sqrt { \frac { \mathrm { w } _ { 2 } } { \mathrm { w } _ { 1 } } \times \frac { l _ { 2 } } { l _ { 1 } } } = \sqrt { \frac { \mathrm { w } _ { 1 } / 2 } { \mathrm { w } _ { 1 } } \times \frac { l _ { 1 } / 2 } { l _ { 1 } } } = \frac { 1 } { 2 }$

$\Rightarrow T _ { 2 } = \frac { T _ { 1 } } { 2 } = 0.5 \mathrm { sec }$