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Questions and Answers
What is the magnetic moment of the needle if it performs 20 complete oscillations in 5 seconds in a uniform magnetic field of 0.049 T?
What is the magnetic moment of the needle if it performs 20 complete oscillations in 5 seconds in a uniform magnetic field of 0.049 T?
- 1.6 × 10^-5 Am^2
- 0.98 × 10^-6 Am^2
- 5.5 × 10^-6 Am^2
- 0.12 × 10^-5 Am^2 (correct)
In the context of oscillations, which of the following quantities is not directly related to the simple harmonic motion of a magnetic needle?
In the context of oscillations, which of the following quantities is not directly related to the simple harmonic motion of a magnetic needle?
- Magnetic field strength
- Moment of inertia
- Gravitational force (correct)
- Frequency of oscillation
Considering a magnetic needle's oscillation, which scenario describes a pair of quantities that share the same dimensions as solid angle?
Considering a magnetic needle's oscillation, which scenario describes a pair of quantities that share the same dimensions as solid angle?
- Strain and arc (correct)
- Force and area
- Stress and strain
- Angular speed and moment of inertia
Which of the following best describes the relationship of a magnetic needle in a uniform magnetic field concerning angular speed?
Which of the following best describes the relationship of a magnetic needle in a uniform magnetic field concerning angular speed?
What is the significance of the disc placed over the surface of water in terms of forces acting on it?
What is the significance of the disc placed over the surface of water in terms of forces acting on it?
What is the moment of inertia of a thin rod about an axis passing through its midpoint and perpendicular to the rod?
What is the moment of inertia of a thin rod about an axis passing through its midpoint and perpendicular to the rod?
If the mass of the bob in a simple pendulum is tripled and its length is halved, how does this affect the time period of oscillation?
If the mass of the bob in a simple pendulum is tripled and its length is halved, how does this affect the time period of oscillation?
What is the relationship between the velocities v1 and v2 if the ratio v1 : v2 is given as 1 : 4?
What is the relationship between the velocities v1 and v2 if the ratio v1 : v2 is given as 1 : 4?
When the length of a pendulum is halved, what is the factor by which the time period changes, assuming mass is constant?
When the length of a pendulum is halved, what is the factor by which the time period changes, assuming mass is constant?
Given a length of 400 g for a rod, what is the estimated length of the rod if its moment of inertia is provided?
Given a length of 400 g for a rod, what is the estimated length of the rod if its moment of inertia is provided?
What is the relationship between the time period (T) of a simple pendulum and its length (L)?
What is the relationship between the time period (T) of a simple pendulum and its length (L)?
If a bob is whirled in a horizontal plane, how does the tension in the string relate to the speed of the bob?
If a bob is whirled in a horizontal plane, how does the tension in the string relate to the speed of the bob?
If the time period of a simple pendulum is $2s$, what will be the new time period if its mass is increased threefold and length is halved?
If the time period of a simple pendulum is $2s$, what will be the new time period if its mass is increased threefold and length is halved?
In a simple harmonic motion, what does the de-Broglie wavelength represent?
In a simple harmonic motion, what does the de-Broglie wavelength represent?
How does increasing the mass of a simple pendulum influence its oscillation period?
How does increasing the mass of a simple pendulum influence its oscillation period?
What happens to the kinetic energy of a particle as its de-Broglie wavelength decreases?
What happens to the kinetic energy of a particle as its de-Broglie wavelength decreases?
For a simple pendulum, if the length is reduced to half its original length, what is the effect on the time period?
For a simple pendulum, if the length is reduced to half its original length, what is the effect on the time period?
If the mass of the rod is 400 g, what is the length if the moment of inertia is given as 2400 g cm?
If the mass of the rod is 400 g, what is the length if the moment of inertia is given as 2400 g cm?
If the time period of a pendulum is T and it is subjected to a mass increase without a change in length, what is the new time period?
If the time period of a pendulum is T and it is subjected to a mass increase without a change in length, what is the new time period?
What is the relationship between the periods of two simple harmonic oscillators if their masses are in the ratio of 1 : 4?
What is the relationship between the periods of two simple harmonic oscillators if their masses are in the ratio of 1 : 4?
For a pendulum, an increase in its length leads to what change in the oscillation frequency?
For a pendulum, an increase in its length leads to what change in the oscillation frequency?
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Study Notes
Magnetic Moment and Time Period of Pendulum
- New magnet's magnetic moment options: M, 2M, M√3, M/50.
- If a pendulum's bob mass is tripled and its length halved, the new oscillation period is x/2 times the original. Identify x from options: √2, 2√3, 4, √3.
Magnetic Field and Inertia
- Magnetic field variations can yield a ratio v: v; options include 2:1, 4:1, 1:4, and 1:2.
- The moment of inertia of a thin rod, given as 2400 g cm², relates to its length and mass; match rod properties with specific length options: 17.5 cm, 20.7 cm, 72.0 cm, 8.5 cm.
Analyzing Angular Motion
- A bob whirled in a horizontal plane at ω rpm creates tension T in the string. True statements are reflected in the correlation between (A) and (R).
Oscillations in Magnetic Fields
- In a 0.049 T uniform magnetic field, a magnetic needle oscillates 20 times in 5 seconds. This gives key metrics for the needle's moment of inertia, linked to a calculated magnetic moment of x × 10⁻⁵ Am².
Dimensional Analysis
- Quantities sharing the same dimensions as solid angle include stresses and angles, strains and arcs, angular speed and stress, versus strains and angles.
Circular Disk Dynamics
- A thin circular disc of radius 4.5 cm interacts with water surface tension, providing a study scenario for surface dynamics and properties.
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