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
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?
Is it possible to have an accelerated motion with a constant speed? Explain
Earth moves around the sun with uniform velocity.
Is it possible to have an accelerated motion with a constant speed? Name such type of motion.
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.
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.
Define Uniform circular motion.
Answer the following question.
Show that the centripetal force on a particle undergoing uniform circular motion is -mrω2.
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) ______.
A particle is perfonning uniform circular motion. If 'θ', 'ω', 'α' and ' a' are its angular displacement, angular velocity, angular acceleration, and centripetal acceleration respectively, then which of the following is 'WRONG'?
A mass 'm' is tied to one end of a spring and whirled in a horizontal circle with constant angular velocity. The elongation in the spring is 1 cm. If the angular speed is doubled, the elongation in the spring is 6 cm. The original length of the spring 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
A body is said to be in nonuniform motion if it travels ______.
The motion of the bus is ______ motion.
For a particle performing uniform circular motion, choose the correct statement(s) from the following:
- Magnitude of particle velocity (speed) remains constant.
- Particle velocity remains directed perpendicular to radius vector.
- Direction of acceleration keeps changing as particle moves.
- Angular momentum is constant in magnitude but direction keeps changing.
What is the direction of the velocity of an object at any point during uniform circular motion?
Angular displacement is measured in which unit?
