Question

The time period of a freely suspended magnet is 4 seconds. If it is broken in length into two equal parts and one part is suspended in the same way, then its time period will be

• A. 4 sec
• B. 2 sec
• C. 0.5 sec
• D. 0.25 sec

Answer 1

Answer: (B)

2 sec

Answer 2

$T = 2 \pi \sqrt { \frac { I } { M B _ { H } } } = 4 \mathrm { sec }$

When magnet is cut into two equal halves, then New magnetic moment $M ^ { \prime } = \frac { M } { 2 }$

New moment of inertia $I ^ { \prime } = \frac { ( \mathrm { w } / 2 ) ( l / 2 ) ^ { 2 } } { 12 } = \frac { 1 } { 8 } \cdot \frac { \mathrm { w } l ^ { 2 } } { 12 }$

Where w is the initial mass of the magnet

But $I = \frac { \mathrm { w } l ^ { 2 } } { 12 } ; \therefore I ^ { \prime } = \frac { I } { 8 }$

$T ^ { \prime } = 2 \pi \sqrt { \frac { I ^ { \prime } } { M ^ { \prime } B _ { H } } }$

$= 2 \pi \sqrt { \frac { I / 8 } { ( M / 2 ) B _ { H } } } = \frac { 1 } { 2 } 2 \pi \sqrt { \frac { I } { M _ { H } } }$ $= \frac { 1 } { 2 } \times T = \frac { 1 } { 2 } \times 4 = 2 \mathrm { sec }$

$T = 2 \pi \sqrt { \frac { I } { M B _ { H } } } = 4 \mathrm { sec }$