Advertisements
Advertisements
प्रश्न
Answer in Brief:
A flywheel used to prepare earthenware pots is set into rotation at 100 rpm. It is in the form of a disc of mass 10 kg and a radius 0.4 m. A lump of clay (to be taken equivalent to a particle) of mass 1.6 kg falls on it and adheres to it at a certain distance x from the center. Calculate x if the wheel now rotates at 80 rpm.
Advertisements
उत्तर
Given:
f1 = 100 rpm,
f2 = 80 rpm,
M = 10 kg,
R = 0.4 m,
m = 1.6 kg
To find:
Value of x
Solution:
I1 = Iwheel = `1/2"MR"^2 = 1/2(10)(0.4)^2 = 0.8` kg.m2
The MI of the wheel and the lump of clay is
I2 = Iwheel + mx2
By the principle of conservation of angular momentum,
I1ω1 = I2ω2
∴ I1(2πf1) = I2(2πf2)
∴ I2 = Iwheel + mx2 = `"f"_1/"f"_2 "I"_1 = "f"_1/"f"_2 "I"_"wheel"`
∴ `"mx"^2 = ("f"_1/"f"_2 - 1)"I"_"wheel" = (100/80 - 1)(0.8)`
`= (5/4 - 1)(0.8) = 0.2` kg.m2
v = x2 = `0.2/1.6 = 1/8`
∴ x = `1/sqrt8`m = 0.3536 m
APPEARS IN
संबंधित प्रश्न
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 ______.
Do we need a banked road for a two-wheeler? Explain.
On what factors does the frequency of a conical pendulum depend? Is it independent of some factors?
While driving along an unbanked circular road, a two-wheeler rider has to lean with the vertical. Why is it so? With what angle the rider has to lean? Derive the relevant expression. Why such a leaning is not necessary for a four wheeler?
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 `sqrt 10` m/s as it travels a distance of `5/3` m along the incline. What can be the possible shape/s of the object?
Does the angle of banking depend on the mass of the vehicle?
A hollow sphere has a radius of 6.4 m. what is the minimum velocity required by a motorcyclist at the bottom to complete the circle.
A bend in a level road has a radius of 100m. find the maximum speed which a car turning this bend may have without skidding if the coefficient of friction between the tires and road is 0.8.
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.
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, ______
When a mass is rotating in a plane about a fixed point, its angular momentum is directed along, ______
Give any two examples of torque in day-to-day life.
What is the relation between torque and angular momentum?
Discuss conservation of angular momentum with example.
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 uniform metallic rod rotates about its perpendicular bisector with constant angular speed. If it is heated uniformly to raise its temperature to a certain value, its speed of rotation ______.
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 ______.
A ring and a disc of different masses are rotating with the same kinetic energy. If we apply a retarding torque τ on the ring, it stops after completing n revolution in all. If the same torque is applied to the disc, how many revolutions would it complete in all before stopping?
What is the difference between rotation and revolution?
