Advertisements
Advertisements
प्रश्न
Solve the following problem.
A particle moves in a circle with a constant speed of 15 m/s. The radius of the circle is 2 m. Determine the centripetal acceleration of the particle.
Advertisements
उत्तर
Given: v = 15 m/s, r = 2m
To find: Centripetal acceleration (a)
Formulae: a = `"v"^2/"r"`
Calculation: From formula,
a = `(15)^2/2 = 225/2`
∴ a = 112.5 m/s2
The centripetal acceleration of the particle is 112.5 m/s2.
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.
Read the statement below carefully and state, with reason, if it is true or false:
The acceleration vector of a particle in uniform circular motion averaged over one cycle is a null vector.
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?
A cyclist is riding with a speed of 27 km/h. As he approaches a circular turn on the road of radius 80 m, he applies brakes and reduces his speed at the constant rate of 0.50 m/s every second. What is the magnitude and direction of the net acceleration of the cyclist on the circular turn?
Explain the meaning of uniform circular motion. Give one example of such motion.
A piece of stone tied at the end of a thread is whirled in a horizontal circle with uniform speed by hand. Answer the following questions:
- Is the velocity of stone uniform or variable?
- Is the acceleration of stone uniform or variable?
- What is the direction of acceleration of stone at any instant?
- Which force provides the centripetal force required for circular motion?
- Name the force and its direction which acts on the hand.
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.
Is it possible to have an accelerated motion with a constant speed? Explain.
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.
Which one of the following is most likely not a case of uniform circular motion?
Consider a simple pendulum of length 4 m. Its bob performs a circular motion in horizontal plane with its string making an angle 60° with the vertical. The Period of rotation of the bob is ____________.(Take g = 10 m/s2)
A body of mass ·m' is moving along a circle of radius 'r' with linear speed 'v'. Now, to change the linear speed to `V/2` and to move it along the circle of radius '4r', required change in the centripetal force of the body is ______.
At any instant, the magnitude of the centripetal force on a particle of mass 'm' performing circular motion is given by (ω = angular velocity and v = linear velocity of the particle) ______.
Two particles P and Q are moving in concentric circles of rarui rp and rQ respectively. If their period of revolutions are in ratio 2 : 3, then ratio of their centripetal acceleration is ____________.
A body moves in a uniform circular motion ______.
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.
Define uniform circular motion and give an example of it. Why is it called accelerated motion?
A flywheel at rest is to reach an angular velocity of 24 rad/s in 8 second with constant angular acceleration. The total angle turned through during this interval is ______.
A cyclist starts from centre O of a circular park of radius 1 km and moves along the path OPRQO as shown figure. If he maintains constant speed of 10 ms–1, what is his acceleration at point R in magnitude and direction?
A particle is given an initial speed u inside a smooth spherical shell of radius R = 1 m that it is just able to complete the circle. Acceleration of the particle when its velocity is vertical is ______.
A disc of radius 5 cm rolls on a horizontal surface with linear velocity v = 1`hat"i"` m/s and angular velocity 50 rad/s. Height of particle from ground on rim of disc which has velocity in vertical direction is ______ cm.
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 ______.
Two bodies of masses 10 kg and 5 kg moving in concentric orbits of radii R and r such that their periods are the same. Then the ratio between their centripetal accelerations is ______.
A body of mass m is moving in circle of radius r with a constant speed v. The work done by the centripetal force in moving the body over half the circumference of the circle is ______.
Why is uniform circular motion said to be accelerated?
Angular displacement is measured in which unit?
