Advertisements
Advertisements
प्रश्न
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?
Advertisements
उत्तर
According to the problem, the path of the cyclist is OPRQO.
The cyclist is in uniform circular motion and it is given that linear velocity = 10 m/s, R = 1 km = 1000 m. As we know whenever an object is performing a circular motion, acceleration is called centripetal acceleration and is always directed towards the centre. So cyclist experiences a centripetal force (acceleration) at point R towards the centre.
The centripetal acceleration at R is given by the relation, `a_c = v^2/r`
⇒ `a_c = (10)^2/1000`
= `100/10^3`
= 0.1 m/s2 along RO.
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.
Give an example of motion in which speed remains uniform, but the velocity changes.
A uniform circular motion is an accelerated motion. Explain it. State whether the acceleration is uniform or variable? Name the force responsible to cause this acceleration. What is the direction of force at any instant? Draw a diagram in support of your answer.
Define angular velocity.
Solve the following problem.
A projectile is thrown at an angle of 30° to the horizontal. What should be the range of initial velocity (u) so that its range will be between 40m and 50 m? Assume g = 10 m s-2.
The angle subtended by the vector A = `5hat"i" + 3hat"j" + 12hat"k"` with the X-axis is ______.
The ratio of angular speed of a hour-hand to the second-hand of a watch is ____________.
A particle performs uniform circular motion in a horizontal plane. The radius of the circle is 8 cm. The centripetal force acting on the particle is 15 N. Its kinetic energy is ____________.
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 ______.
A stone of mass 3 kg attached at one end of a 2m long string is whirled in horizontal circle. The string makes an angle of 45° with the vertical then the centripetal force acting on the string is ______.
(g = 10 m/s2 , tan 45° = 1)
A cyclist is riding with a speed of 43.2 km/h. As he approaches a circular turn on the road of radius 60 m, he applies brakes and reduces his speed at constant rate of 1.8 ms-2. The magnitude of the net acceleration of the cyclist is ______.
A body is said to be in nonuniform motion if it travels ______.
Define uniform circular motion and give an example of it. Why is it called accelerated motion?
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 small bead of mass m can move on a smooth circular wire (radius R) under the action of a force F = `"Km"/"r"^2` directed (r = position of bead r from P and K = constant) towards a point P within the circle at a distance R/2 from the centre. The minimum velocity should be ______ m/s of bead at the point of the wire nearest the centre of force (P) so that bead will complete the circle. (Take `"k"/(3"R")` = 8 unit)
A ceiling fan rotates about its own axis with some angular velocity. When the fan is switched off the angular velocity becomes `(1/4)^"th"` of the original in time 't' and 'n' revolutions are made in that time. The number of revolutions made by the fan during the time interval between switch off and rest are ______. (Angular retardation is uniform)
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?
