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.
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.
On what factors does the frequency of a conical pendulum depend? Is it independent of some factors?
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)
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.
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 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 rigid body rotates with an angular momentum L. If its kinetic energy is halved, the angular momentum becomes, ______
Give any two examples of torque in day-to-day life.
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 ______.
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?
