Advertisements
Advertisements
प्रश्न
A stone tied to the end of a string 80 cm long is whirled in a horizontal circle with a constant speed. If the stone makes 14 revolutions in 25 s, what is the magnitude and direction of acceleration of the stone?
Advertisements
उत्तर
Length of the string, l = 80 cm = 0.8 m
Number of revolutions = 14
Time taken = 25 s
Frequency v = `"Number of revolution"/"Time taken" = 14/25 Hz`
Angular frequency, ω = 2πν
`2xx22/7xx14/25 = 88/25 rads^(-1)`
Centripetal acceleration, `a_c = omega^2 r`
=`(88/25)^2 xx 0.8`
= `0.80 xx 88/25 xx 88/25`
= 9.90 `ms^(-2)`
The direction of centripetal acceleration is always directed along the string, toward the centre, at all points.
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.
Draw a neat labelled diagram of conical pendulum. State the expression for its periodic time in terms of length.
Is it possible to have an accelerated motion with a constant speed? Explain
Differentiate between uniform linear motion and uniform circular motion.
In a uniform circular motion, the speed continuously changes because of the direction of motion changes.
What is a conical pendulum?
A particle is moving in uniform circular motion with speed 'V' and radius 'R'. The angular acceleration of the particle is ______.
Select the WRONG statement.
It is possible to have objects moving with uniform velocity but non-uniform acceleration.
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 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?
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 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 ______.
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)
Why is uniform circular motion said to be accelerated?
What is the direction of the velocity of an object at any point during uniform circular motion?
By applying Kepler's third law to the formula for centripetal force, Newton concluded that the force acting on a planet is:
