Advertisements
Advertisements
प्रश्न
A vehicle is moving on a circular track whose surface is inclined towards the horizon at an angle of 10°. The maximum velocity with which it can move safely is 36 km / hr. Calculate the length of the circular track. [π = 3.142]
Advertisements
उत्तर
Given, angle of banking, θ = 10°
Optimum speed, V0 = 36 km/hr = 36 x `5/18` m/s.
Or, V0 = 10 m/s
Let R be the radius of the circular track
We have,
V0 = `sqrt( gRtanθ )`
⇒ `V_0^2` = gRtanθ
⇒ R = `V_0^2/[ g tanθ ]`
= `(10m/s)^2/[(9.8m/s^2) xx tan 10^0]`
= `[100m]/[ 9.8 xx 0.1763 ]`
⇒ R = 57.88 m
∴ Length of the circular track = 2πR = 2 x 3.142 x 57.88 = 363.72m.
APPEARS IN
संबंधित प्रश्न
In U. C. M (Uniform Circular Motion), prove the relation `vec v = vec w xx vec r`, where symbols have their usual meanings.
A particle starts from the origin at t = 0 s with a velocity of 10.0 `hatj "m/s"` and moves in the x-y plane with a constant acceleration of `(8.0 hati + 2.0 hatj) ms^(-2)`.
- At what time is the x-coordinate of the particle 16 m? What is the y-coordinate of the particle at that time?
- What is the speed of the particle at the time?
Earth moves around the sun with uniform velocity.
Give an example of motion in which speed remains uniform, but the velocity changes.
State True or False
The earth moves around the sun with a uniform.
A uniform linear motion is unaccelerated, while a uniform circular motion is an accelerated motion.
Complete a sentence and explain it.
When an object is in uniform circular motion, its ______ changes at every point.
Which of the following remains constant in a uniform circular motion, Speed or Velocity, or both?
Define Uniform circular motion.
Answer the following question.
Show that its time period is given by, 2π`sqrt((l cos theta)/("g"))` where l is the length of the string, θ is the angle that the string makes with the vertical, and g is the acceleration due to gravity.
Define angular velocity.
A particle goes round a circular path with uniform speed v. After describing half the circle, what is the change in its centripetal acceleration?
The ratio of the angular speed of minute hand and hour hand of a watch is ____________.
A disc has mass 'M' and radius 'R'. How much tangential force should be applied to the rim of the disc, so as to rotate with angular velocity 'ω' in time t?
A string of length 'l' fixed at one end carries a mass 'm' at the other end. The string makes `3/pi` revolutions/second around the vertical axis through the fixed end as shown in figure. The tension 'T' in the string is ______.
Which of the following is correct about uniform circular motion
- the direction of motion is continuously changed
- the direction of motion is not changed
- speed and direction both remain constant
- speed is constant but the direction is changing
The motion of the bus is ______ motion.
It is possible to have objects moving with uniform velocity but non-uniform acceleration.
A point object moves along an arc of a circle of radius 'R'. Its velocity depends upon the distance covered 'S' as V = `Ksqrt(S)` where 'K' is a constant. If 'e' is the angle between the total acceleration and tangential acceleration, then
A body moving along a circular path of radius R with velocity v, has centripetal acceleration a. If its velocity is made equal to 2v. What will be the centripetal acceleration?
If a body is moving in a circle of radius r with a constant speed v, its angular velocity is ______.
Earth also moves in circular orbit around sun once every year with on orbital radius of 1.5 × 1011 m. What is the acceleration of earth (or any object on the surface of the earth) towards the centre of the sun? How does this acceleration compare with g = 9.8 m/s2?
A wet open umbrella is held upright and is rotated about the handle at a uniform rate of 21 revolutions in 44 s. If the rim of the umbrella is a circle of 1 metre in diameter and the height of the rim above the floor is 1.5 m, the drops of water spun off the rim and hit the floor at a horizontal ______ m from the umbrella.
A wheel rotating at the same angular speed undergoes constant angular retardation. After the revolution, angular velocity reduces to half its initial value. It will make ______ revolution before stopping.
The distance of the Sun from earth is 1.5 × 1011 m and its angular diameter is (2000) s when observed from the earth. The diameter of the Sun will be ______.
A rod PQ of mass M and length L is hinged at end P. The rod is kept horizontal by a massless string tied to point Q as shown in figure. When string is cut, the initial angular acceleration of the rod is ______.
In uniform circular motion, although the speed is constant, why does acceleration occur?
A particle moving with uniform speed in a circular path maintains ______.
