Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Given:
Radius of curve, r = 1 km = 1000 m,
Speed of train, v = 36 km/hr = `36 xx 5/18` = 10 m/s
To find: Elevation of rails (h)
Formulae:
- tan θ = `"v"^2/"rg"`
- h = l sinθ
Calculation:
From formula (i),
θ = `tan^-1("v"^2/"rg")`
= `tan^-1(100/(1000 xx 9.8))`
= `tan^-1(1/98)`
= `tan^-1(10^-1/98)`
= `tan^-1(0.1020 xx 10^-1)`
= `tan^-1(0.01020)`
∴ θ = 0°35'
From formula (ii),
h = l sin θ
h = 1 × sin (0°35′)
= 0.0102 m
∴ h = 1.02 cm
The elevation of the outer rail above the inner rail is 1.02 cm.
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.
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?
During ice ballet, while in the outer rounds, why do the dancers outstretch their arms and legs.
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 maximum safety speed with which a vehicle should move along a curved horizontal road. State the significance of it.
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, ______
What is the relation between torque and angular momentum?
What are the rotational equivalents for the physical quantities, (i) mass and (ii) force?
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 ______.
What is the difference between rotation and revolution?
