Question:
Two identical bar magnets are placed one above the other such that they are mutually perpendicular and bisect each other. The time period of this combination in a horizontal magnetic field is 'T'. The time period of each magnet in the same field is:
Two identical bar magnets are placed one above the other such that they are mutually perpendicular and bisect each other. The time period of this combination in a horizontal magnetic field is 'T'. The time period of each magnet in the same field is:
Show Hint
When combining magnets perpendicularly, the resultant magnetic moment adds vectorially, while their moments of inertia add arithmetically.
Updated On: Jun 9, 2026
- \( \sqrt{2}T \)
- \( 2^{(1/4)}T \)
- \( 2^{-(1/3)}T \)
- \( 2^{-(1/4)}T \)
Show Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Concept:
The time period of an oscillating magnet in a magnetic field \( B \) is \( T = 2\pi \sqrt{\frac{I}{\mu B}} \), where \( I \) is the moment of inertia and \( \mu \) is the magnetic moment.
Step 1: Analyze the combination.
For the combination, the total moment of inertia \( I_{comb} = I_1 + I_2 = 2I \) (since they are identical). The total magnetic moment \( \mu_{comb} \) is the vector sum: \( \mu_{comb} = \sqrt{\mu^2 + \mu^2} = \mu\sqrt{2} \). $$ T = 2\pi \sqrt{\frac{2I}{\mu\sqrt{2}B}} = 2\pi \sqrt{\frac{I\sqrt{2}}{\mu B}} = T_0 (2)^{1/4} $$ where \( T_0 \) is the time period of a single magnet \( 2\pi \sqrt{\frac{I}{\mu B}} \).
Step 2: Solve for \( T_0 \).
$$ T = T_0 \cdot 2^{1/4} \implies T_0 = T \cdot 2^{-1/4} $$ $$\boxed{2^{-(1/4)}T}$$
Step 1: Analyze the combination.
For the combination, the total moment of inertia \( I_{comb} = I_1 + I_2 = 2I \) (since they are identical). The total magnetic moment \( \mu_{comb} \) is the vector sum: \( \mu_{comb} = \sqrt{\mu^2 + \mu^2} = \mu\sqrt{2} \). $$ T = 2\pi \sqrt{\frac{2I}{\mu\sqrt{2}B}} = 2\pi \sqrt{\frac{I\sqrt{2}}{\mu B}} = T_0 (2)^{1/4} $$ where \( T_0 \) is the time period of a single magnet \( 2\pi \sqrt{\frac{I}{\mu B}} \).
Step 2: Solve for \( T_0 \).
$$ T = T_0 \cdot 2^{1/4} \implies T_0 = T \cdot 2^{-1/4} $$ $$\boxed{2^{-(1/4)}T}$$
Was this answer helpful?
0
0
Top AP EAPCET Physics Questions
- A body is projected from the ground at an angle of $\tan^{-1} \left( \frac{8}{7}\right)$ with the horizontal. The ratio of the maximum height attained by it to its range is
- A lens forms real and virtual images of an object, when the object is at $u_{1}$ and $u_{2}$ distances respectively. If the size of the virtual image is double that of the real image, then the focal length of the lens is (take, the magnification of the real image as $m$ )
- Two spheres $P$ and $Q$, each of mass $200\, g$ are attached to a string of length one metre as shown in the figure. The string and the spheres are then whirled in a horizontal circle about $O$ at a constant angular speed. The ratio of the tension in the string between $P$ and $Q$ to that of between $P$ and $O$ is $(P$ is at mid-point of the line joining $O$ and $Q$ )
- The radii of the two columns in a U - tube are r1 and r2. When a liquid of density p (angle of contact is $ 0{}^\circ $ ) is filled in it, the level difference of the liquid in the two arms is h. The surface tension of the liquid is: (g = acceleration due to gravity)
- A rigid metallic sphere is spinning around its own axis in the absence of external torque. If the temperature is raised, its volume increases by $9 \%$. The change in its angular speed is
View More Questions
Top AP EAPCET Magnetic Effects of Current and Magnetism Questions
- If the magnetic field is along the positive y-axis and the electron is moving along the positive x-axis, the direction of force on the electron is
- A bar magnet of length \(0.1~\text{m}\) and magnetic moment of \(5~\text{Am}^2\) is placed in a uniform magnetic field of intensity \(0.4~\text{T}\), with its axis making an angle of \(60^\circ\) with the field. The torque on the magnet is
- A flexible wire loop carrying current is placed in external magnetic field. Its shape becomes:
- A straight wire carrying a current of 12 A is bent into a semi-circular arc of radius 2 cm as shown in the figure. Then the magnetic field due to the straight segments at the centre of the arc is
- A charged particle of mass \( m \) and charge \( q \) moves with a velocity \( \vec{v} \) perpendicular to a magnetic field \( \vec{B} \). The radius of the circular path it follows is:
View More Questions
Top AP EAPCET Questions
- A body is projected from the ground at an angle of $\tan^{-1} \left( \frac{8}{7}\right)$ with the horizontal. The ratio of the maximum height attained by it to its range is
- The four quantum numbers of the valence electron of potassium are :
- A lens forms real and virtual images of an object, when the object is at $u_{1}$ and $u_{2}$ distances respectively. If the size of the virtual image is double that of the real image, then the focal length of the lens is (take, the magnification of the real image as $m$ )
- Two spheres $P$ and $Q$, each of mass $200\, g$ are attached to a string of length one metre as shown in the figure. The string and the spheres are then whirled in a horizontal circle about $O$ at a constant angular speed. The ratio of the tension in the string between $P$ and $Q$ to that of between $P$ and $O$ is $(P$ is at mid-point of the line joining $O$ and $Q$ )
- The volume of $0.02\, M$ acidified permanganate solution required for complete reaction of $60\, mL$ of $0.01\, MI^{-}$ ion solution to form $I_2$ in $mL$ is
View More Questions