Advertisements
Advertisements
प्रश्न
The coefficient of static friction between a coin and a gramophone disc is 0.5. Radius of the disc is 8 cm. Initially the center of the coin is 2 cm away from the center of the disc. At what minimum frequency will it start slipping from there? By what factor will the answer change if the coin is almost at the rim? (use g = π2m/s2)
Advertisements
उत्तर
Given: μs = 0.5
rD = 8 cm = 8 × 10−2 m
rC = 2 cm = 2 × 10−2 m
Fmin = ?
mrω2 = μN
mrω2 = μ mg ...[N = mg]
∴ ω2 = `(mu g)/r`
⇒ 4 π2 f2 = `(0.5 xx pi^2)/(2 xx 10^-2)` ...[ω = 2 π f ⇒ ω2 = 22 π2 f2 ⇒ ω2 = 4 π2 f2]
⇒ `4 cancel(pi^2)f^2 = (0.5 xx cancel(pi^2))/(2 xx 10^-2)`
⇒ f2 = `(0.5 xx 10^2)/(4 xx 2)`
⇒ f2 = `50/8`
⇒ f2 = `25/4`
⇒ f = `5/2 = 2.5` rev/s
`f prop 1/sqrtr, f_n prop 1/sqrt(r_n)`
`f_n/f = sqrt(r/r_n)`
= `sqrt((2 xx 10^-2)/(8 xx 10^-2))`
= `sqrt(1/4)`
fn = `1/2 f`
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 ______.
Answer in brief:
Why are curved roads banked?
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?
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.
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.
What is a conical pendulum? Obtain an expression for its time period
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, ______
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?
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 ______.
What is the difference between rotation and revolution?
