A thin circular disk is in the $xy$ plane as shown in the figure. The ratio of its moment of inertia about $z$ and $z'$ axes will be :
- 1:03
- 1:04
- 1:05
- 1:02
The Correct Option is A
Solution and Explanation
Top Questions on System of Particles & Rotational Motion
- Two iron solid discs of negligible thickness have radii \( R_1 \) and \( R_2 \) and moment of inertia \( I_1 \) and \( I_2 \), respectively. For \( R_2 = 2R_1 \), the ratio of \( I_1 \) and \( I_2 \) would be \( \frac{1}{x} \), where \( x \) is:
- JEE Main - 2025
- Physics
- System of Particles & Rotational Motion
- Match List - I with List - II: List - I:
- (A) Electric field inside (distance \( r > 0 \) from center) of a uniformly charged spherical shell with surface charge density \( \sigma \), and radius \( R \).
- (B) Electric field at distance \( r > 0 \) from a uniformly charged infinite plane sheet with surface charge density \( \sigma \).
- (C) Electric field outside (distance \( r > 0 \) from center) of a uniformly charged spherical shell with surface charge density \( \sigma \), and radius \( R \).
- (D) Electric field between two oppositely charged infinite plane parallel sheets with uniform surface charge density \( \sigma \).
- (I) \( \frac{\sigma}{\epsilon_0} \)
- (II) \( \frac{\sigma}{2\epsilon_0} \)
- (III) 0
- (IV) \( \frac{\sigma}{\epsilon_0 r^2} \)
- JEE Main - 2025
- Physics
- System of Particles & Rotational Motion
- The center of mass of a thin rectangular plate (fig - x) with sides of length \( a \) and \( b \), whose mass per unit area (\( \sigma \)) varies as \( \sigma = \sigma_0 \frac{x}{ab} \) (where \( \sigma_0 \) is a constant), would be
- JEE Main - 2025
- Physics
- System of Particles & Rotational Motion
- The moment of inertia of a solid disc rotating along its diameter is 2.5 times higher than the moment of inertia of a ring rotating in a similar way. The moment of inertia of a solid sphere which has the same radius as the disc and rotating in similar way, is \( n \) times higher than the moment of inertia of the given ring. Here, \( n = \):
- JEE Main - 2025
- Physics
- System of Particles & Rotational Motion
- The increase in pressure required to decrease the volume of a water sample by 0.2percentage is \( P \times 10^5 \, \text{Nm}^{-2} \). Bulk modulus of water is \( 2.15 \times 10^9 \, \text{Nm}^{-2} \). The value of \( P \) is ________________.
- JEE Main - 2025
- Physics
- System of Particles & Rotational Motion
Questions Asked in JEE Main exam
In the experiment for measurement of viscosity \( \eta \) of a given liquid with a ball having radius \( R \), consider following statements:
A. Graph between terminal velocity \( V \) and \( R \) will be a parabola.
B. The terminal velocities of different diameter balls are constant for a given liquid.
C. Measurement of terminal velocity is dependent on the temperature.
D. This experiment can be utilized to assess the density of a given liquid.
E. If balls are dropped with some initial speed, the value of \( \eta \) will change.- JEE Main - 2025
- Fluid Mechanics
Given below are two statements: one is labelled as Assertion \(A\) and the other as Reason \(R\):
Assertion \(A\): A sound wave has higher speed in solids than in gases.
Reason \(R\): Gases have higher value of Bulk modulus than solids.- JEE Main - 2025
- Fluid Mechanics
- Consider \( I_1 \) and \( I_2 \) are the currents flowing simultaneously in two nearby coils 1 & 2, respectively. If \( L_1 \) = self inductance of coil 1, \( M_{12} \) = mutual inductance of coil 1 with respect to coil 2, then the value of induced emf in coil 1 will be:
- JEE Main - 2025
- Fluid Mechanics
- A proton of mass 'mp' has same energy as that of a photon of wavelength 'λ'. If the proton is moving at non-relativistic speed, then ratio of its de Broglie wavelength to the wavelength of photon is.
- JEE Main - 2025
- Fluid Mechanics
A bead of mass \( m \) slides without friction on the wall of a vertical circular hoop of radius \( R \) as shown in figure. The bead moves under the combined action of gravity and a massless spring \( k \) attached to the bottom of the hoop. The equilibrium length of the spring is \( R \). If the bead is released from the top of the hoop with (negligible) zero initial speed, the velocity of the bead, when the length of spring becomes \( R \), would be (spring constant is \( k \), \( g \) is acceleration due to gravity):
- JEE Main - 2025
- Fluid Mechanics
Concepts Used:
System of Particles and Rotational Motion
- The system of particles refers to the extended body which is considered a rigid body most of the time for simple or easy understanding. A rigid body is a body with a perfectly definite and unchangeable shape.
- The distance between the pair of particles in such a body does not replace or alter. Rotational motion can be described as the motion of a rigid body originates in such a manner that all of its particles move in a circle about an axis with a common angular velocity.
- The few common examples of rotational motion are the motion of the blade of a windmill and periodic motion.