Advertisements
Advertisements
Question
On what factors does the frequency of a conical pendulum depend? Is it independent of some factors?
Solution
Expression for a frequency of canonical pendulum is given as:
f = `1/(2pi) sqrt("g"/("L cos" theta)`
Here, f is the frequency, l is the length of pendulum and g is the acceleration due to gravity, and θ is the angle of inclination.
From the above expression, we can see that
- The frequency is directly proportional to the root of the acceleration due to gravity `f oo sqrtg`.
- The frequency is inversely proportional to the length of the length of the pendulum `f oo sqrt("I"/l)`.
- The frequency is inversely related to the angle of inclination `f oo sqrt(1/ (cos theta))`
- The frequency does not depend on the mass of the bob.
APPEARS IN
RELATED QUESTIONS
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 ______.
Answer in brief:
Why are curved roads banked?
Do we need a banked road for a two-wheeler? Explain.
Somehow, an ant is stuck to the rim of a bicycle wheel of diameter 1 m. While the bicycle is on a central stand, the wheel is set into rotation and it attains the frequency of 2 rev/s in 10 seconds, with uniform angular acceleration. Calculate:
- The number of revolutions completed by the ant in these 10 seconds.
- Time is taken by it for first complete revolution and the last complete revolution.
Starting from rest, an object rolls down along an incline that rises by 3 in every 5 (along with it). The object gains a speed of `sqrt10` m/s as it travels a distance of `5/3` m along the incline. What can be the possible shape/s of the object?
A big dumb-bell is prepared by using a uniform rod of mass 60 g and length 20 cm. Two identical solid spheres of mass 25 g and radius 10 cm each are at the two ends of the rod. Calculate the moment of inertia of the dumb-bell when rotated about an axis passing through its centre and perpendicular to the length.
During ice ballet, while in the outer rounds, why do the dancers outstretch their arms and legs.
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.
A body weighing 0.5 kg tied to a string is projected with a velocity of 10 m/s. The body starts whirling in a vertical circle. If the radius of the circle is 0.8 m, find the tension in the string when the body is at the top of the circle.
Derive an expression for the kinetic energy of a rotating body with uniform angular velocity.
A railway track goes around a curve having a radius of curvature of 1 km. The distance between the rails is 1 m. Find the elevation of the outer rail above the inner rail so that there is no side pressure against the rails when a train goes around the curve at 36 km/hr.
Obtain an expression for maximum safety speed with which a vehicle can be safely driven along a curved banked road.
A rigid body rotates with an angular momentum L. If its kinetic energy is halved, the angular momentum becomes, ______
A particle undergoes uniform circular motion. The angular momentum of the particle remains conserved about, ______
What is the relation between torque and angular momentum?
What are the rotational equivalents for the physical quantities, (i) mass and (ii) force?
A flywheel rotates with uniform angular acceleration. If its angular velocity increases from `20pi` rad/s to `40pi` rad/s in 10 seconds. Find the number of rotations in that period.
A wheel of radius 2 cm is at rest on the horizontal surface. A point P on the circumference of the wheel is in contact with the horizontal surface. When the wheel rolls without slipping on the surface, the displacement of point P after half rotation of wheel is ______.
