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Two bodies have their moments of inertia I and 2I respectively about their axis of rotation. If their kinetic energies of rotation are equal, then what is the ratio of their angular velocity.
Concept: Moment of Inertia as an Analogous Quantity for Mass
A bucket containing water is tied to one end of a rope 5 m long and it is rotated in a vertical circle about the other end. Find the number of rotations per minute in order that the water in the bucket may not spill.
Concept: Rotational Dynamics
A flywheel of mass 8 kg and radius 10 cm rotating with a uniform angular speed of 5 rad/sec about its axis of rotation, is subjected to an accelerating torque of 0.01 Nm for 10 seconds. Calculate the change in its angular momentum and change in its kinetic energy.
Concept: Angular Momentum or Moment of Linear Momentum
What is a conical pendulum? Obtain an expression for its time period
Concept: Rotational Dynamics
Obtain an expression for maximum safety speed with which a vehicle can be safely driven along a curved banked road.
Concept: Rotational Dynamics
When the bob performs a vertical circular motion and the string rotates in a vertical plane, the difference in the tension in the string at horizontal position and uppermost position is ______.
Concept: Vertical Circular Motion
Calculate the moment of inertia of a uniform disc of mass 10 kg and radius 60 cm about an axis perpendicular to its length and passing through its center.
Concept: Moment of Inertia as an Analogous Quantity for Mass
An electron in an atom is revolving round the nucleus in a circular orbit of radius 5.3 × 10-11 m with a speed of 3 × 106 m/s. Find the angular momentum of electron.
Concept: Angular Momentum or Moment of Linear Momentum
If friction is made zero for a road, can a vehicle move safely on this road?
Concept: Applications of Uniform Circular Motion
Derive expressions for the linear velocity at the lowest position, mid-way position and top-most position for a particle revolving in a vertical circle, if it has to just complete circular motion without string slackening at the top.
Concept: Vertical Circular Motion
A ceiling fan has a moment of inertia of 2 kg. m2. It attains maximum frequency of 60 r.p.m. in 2π seconds. Calculate its power rating.
Concept: Conservation of Angular Momentum
State and prove the theorem of the parallel axis about the moment of inertia.
Concept: Theorems of Perpendicular and Parallel Axes
Calculate the change in angular momentum of the electron when it jumps from third orbit to first orbit in hydrogen atom.
(Take h = 6.33 × 10−34 Js)
Concept: Angular Momentum or Moment of Linear Momentum
The moment of inertia (MI) of a disc of radius R and mass M about its central axis is ______.
Concept: Moment of Inertia as an Analogous Quantity for Mass
Define centripetal force.
Concept: Circular Motion and Its Characteristics
Derive an expression for maximum speed moving along a horizontal circular track.
Concept: Applications of Uniform Circular Motion
A horizontal force of 0.5 N is required to move a metal plate of area 10−2 m2 with a velocity of 3 × 10−2m/s, when it rests on 0.5 × 10−3 m thick layer of glycerin. Find the coefficient of viscosity of glycerin.
Concept: Applications of Uniform Circular Motion
The radius of a circular track is 200 m. Find the angle of banking of the track, if the maximum speed at which a car can be driven safely along it is 25 m/sec.
Concept: Applications of Uniform Circular Motion
The energy of the free surface of a liquid drop is 5π times the surface tension of the liquid. Find the diameter of the drop in C.G.S. system.
Concept: Surface Tension
A sonometer wire vibrates with frequency n1 in air under suitable load of specific gravity of . When the load is immersed in water, the frequency of vibration of wire n2 will be .........
Concept: Variation in the Acceleration>Variation in Gravity with Altitude
