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The difference in tensions in the string at lowest and highest points in the path of the particle of mass 'm' performing vertical circular motion is:....
a) 2 mg
b) 4 mg
c) 6 mg
d) 8 mg
Concept: Vertical Circular Motion Due to Earth’s Gravitation
A stone of mass 2 kg is whirled in a horizontal circle attached at the end of 1.5m long string. If the string makes an angle of 30° with vertical, compute its period. (g = 9.8 m/s2)
Concept: Rolling Motion
Obtain an expression for torque acting on a body rotating with uniform angular acceleration.
Concept: Angular Momentum or Moment of Linear Momentum
The speed limit for a vehicle on road is 120 km/ hr. A policeman detects a drop of 10% in the pitch of horn of a car as it passes him. Is the policeman justified in punishing the car driver for crossing the speed limit? (Given: Velocity of sound= 340 m/s)
Concept: Equation for Velocity and Energy at Different Positions of Vertical Circular Motion
A racing car completes 5 rounds of a circular track in 2 minutes. Find the radius of the track
if the car has uniform centripetal acceleration of Π2 m/s2.
Concept: Dynamics of Uniform Circular Motion - Centripetal Force
Define radius of gyration.
Concept: Radius of Gyration
A planet is revolving around a star in a circular orbit of radius R with a period T. If the
gravitational force between the planet and the star is proportional to `R^(-3/2)` then
A) `T^2 prop R^(5/2)`
B) `T^2 prop R^((-7)/2)`
C) `T^2 prop R^(3/2)`
D) `T^2 prop R^4`
Concept: Vertical Circular Motion Due to Earth’s Gravitation
A particle of mass m performs the vertical motion in a circle of radius r. Its potential energy at the highest point is _______. (g is acceleration due to gravity)
Concept: Vertical Circular Motion Due to Earth’s Gravitation
Distinguish between centripetal and centrifugal force.
Concept: Centrifugal Forces
A falt curve on a highways has a radius of curvature 400 m. A car goes around a curve at a speed of 32 m/s. What is the minimum value of the coefficient of friction that will prevent the car from sliding? (g = 9.8 m/s2)
Concept: Banking of Roads
What is the value of tangential acceleration in U.C.M.?
Concept: Angular Acceleration
Obtain expressions of energy of a particle at different positions in the vertical circular motion .
Concept: Vertical Circular Motion Due to Earth’s Gravitation
A particle of mass 1 kg, tied to a 1.2 m long string is whirled to perform the vertical circular motion, under gravity. The minimum speed of a particle is 5 m/s. Consider the following statements.
P) Maximum speed must be `5sqrt5` m/s.
Q) Difference between maximum and minimum tensions along the string is 60 N.
Select the correct option.
Concept: Circular Motion and Its Characteristics
A thin walled hollow cylinder is rolling down an incline, without slipping. At any instant, without slipping. At any instant, the ratio "Rotational K.E.: Translational K.E.: Total K.E." is ______.
Concept: Rotational Dynamics
Do we need a banked road for a two-wheeler? Explain.
Concept: Rotational Dynamics
Answer in brief:
Derive an expression which relates angular momentum with the angular velocity of a rigid body.
Concept: Conservation of Angular Momentum
Discuss the interlink between translational, rotational and total kinetic energies of a rigid object rolls without slipping.
Concept: Rolling Motion
A diver in a swimming pool bends his head before diving. It ______.
Concept: Moment of Inertia as an Analogous Quantity for Mass
A stone is tied to one end of a string. Holding the other end, the string is whirled in a horizontal plane with progressively increasing speed. It breaks at some speed because ______
Concept: Angular Momentum or Moment of Linear Momentum
During ice ballet, while in the outer rounds, why do the dancers outstretch their arms and legs.
Concept: Rotational Dynamics
