Advertisements
Advertisements
प्रश्न
A particle of mass 1 kg, tied to a 1.2 m long string is whirled to perform the vertical circular motion, under gravity. The minimum speed of a particle is 5 m/s. Consider the following statements.
P) Maximum speed must be `5sqrt5` m/s.
Q) Difference between maximum and minimum tensions along the string is 60 N.
Select the correct option.
विकल्प
Only the statement P is correct.
Only the statement Q is correct.
Both the statements are correct.
Both the statements are incorrect.
Advertisements
उत्तर
Only the statement Q is correct.
Explanation:
The minimum speed of the particle = `v_A` = 5 m/s
The length of the string (h) = 2.4 m
The radius (l) = 1.2 m
The mass of the particle, m = 1 kg
Conserving energy between A and B
⇒ `1/2 mv_A^2 + mgh = 1/2mv_B^2 + 0`
⇒ `v_A^2 + 2gh = v_B^2`
⇒ `5^2 + 2 xx 9.8 xx 2.4 = v_B^2`
⇒ `v_B^2 = 72`
⇒ `v_B = sqrt72` m/s
At point B,
`T_B - mg = (mv_B^2)/r`
`T_B = (mv_B^2)/r + mg` ...(1)
At point A,
`T_A + mg = (mv_A^2)/r`
`T_A = (mv_A^2)/r - mg` ...(2)
`T_B - T_A = ((mv_B^2)/r + mg) - ((mv_A^2)/r - mg)`
= `m/r (v_B^2 - v_A^2) + 2mg`
= `1/1.2 (72 - 25) + 2(1)(9.8)`
= 60 N
संबंधित प्रश्न
You may have seen in a circus a motorcyclist driving in vertical loops inside a ‘death-well’ (a hollow spherical chamber with holes, so the spectators can watch from outside). Explain clearly why the motorcyclist does not drop down when he is at the uppermost point, with no support from below. What is the minimum speed required at the uppermost position to perform a vertical loop if the radius of the chamber is 25 m?
Water in a bucket is whirled in a vertical circle with string attached to it. The water does no fall down even when the bucket is inverted at the top of its path. We conclude that in this position
A coin placed on a rotating turntable just slips. If it is placed at a distance of 4 cm from the centre. If the angular velocity of the turntable is doubled, it will just slip at a distance of
A motorcycle is going on an overbridge of radius R. The driver maintains a constant speed. As the motorcycle is ascending on the overbridge, the normal force on it
A train A runs from east to west and another train B of the same mass runs from west to east at the same speed along the equator. A presses the track with a force F1 and B presses the track with a force F2.
A simple pendulum having a bob of mass m is suspended from the ceiling of a car used in a stunt film shooting. the car moves up along an inclined cliff at a speed v and makes a jump to leave the cliff and lands at some distance. Let R be the maximum height of the car from the top of the cliff. The tension in the string when the car is in air is
An object follows a curved path. The following quantities may remain constant during the motion
(a) speed
(b) velocity
(c) acceleration
(d) magnitude of acceleration.
Find the acceleration of the moon with respect to the earth from the following data:
Distance between the earth and the moon = 3.85 × 105 km and the time taken by the moon to complete one revolution around the earth = 27.3 days.
Find the acceleration of a particle placed on the surface of the earth at the equator due to earth's rotation. The diameter of earth = 12800 km and it takes 24 hours for the earth to complete one revolution about its axis.
A scooter weighing 150 kg together with its rider moving at 36 km/hr is to take a turn of a radius 30 m. What horizontal force on the scooter is needed to make the turn possible ?
The bob of a simple pendulum of length 1 m has mass 100 g and a speed of 1.4 m/s at the lowest point in its path. Find the tension in the string at this instant.
A turn of radius 20 m is banked for the vehicles going at a speed of 36 km/h. If the coefficient of static friction between the road and the tyre is 0.4, what are the possible speeds of a vehicle so that it neither slips down nor skids up?
A motorcycle has to move with a constant speed on an over bridge which is in the form of a circular arc of radius R and has a total length L. Suppose the motorcycle starts from the highest point.(a) What can its maximum velocity be for which the contact with the road is not broken at the highest point? (b) If the motorcycle goes at speed 1/√2 times the maximum found in part (a), where will it lose the contact with the road? (c) What maximum uniform speed can it maintain on the bridge if it does not lose contact anywhere on the bridge?
A car goes on a horizontal circular road of radius R, the speed increasing at a constant rate \[\frac{\text{dv}}{\text{dt}} = a\] . The friction coefficient between the road and the tyre is μ. Find the speed at which the car will skid.
A block of mass m moves on a horizontal circle against the wall of a cylindrical room of radius R. The floor of the room on which the block moves is smooth but the friction coefficient between the wall and the block is μ. The block is given an initial speed v0. As a function of the speed v writes
(a) the normal force by the wall on the block,
(b) the frictional force by a wall, and
(c) the tangential acceleration of the block.
(d) Integrate the tangential acceleration \[\left( \frac{dv}{dt} = v\frac{dv}{ds} \right)\] to obtain the speed of the block after one revolution.
A person stands on a spring balance at the equator. If the speed of earth's rotation is increased by such an amount that the balance reading is half the true weight, what will be the length of the day in this case?
When seen from below, the blades of a ceiling fan are seen to be revolving anticlockwise and their speed is decreasing. Select the correct statement about the directions of its angular velocity and angular acceleration.
Choose the correct option.
Consider the following cases:
(P) A planet revolving in an elliptical orbit.
(Q) A planet revolving in a circular orbit.
Principle of conservation of angular momentum comes in force in which of these?
The escape velocity of a body from any planet, whose mass is six times the mass of earth and radius is twice the radius of earth will be
(v8 = escape velocity of a body from the earth's surface).
The real force 'F' acting on a particle of mass ' m' performing circular motion acts along the radius of circle 'r' and is directed towards the centre of circle. The square root of the magnitude of such force is (T = periodic time).
The centripetal force of a body moving in a circular path, if speed is made half and radius is made four times the original value, will ____________.
A particle performs uniform circular motion in a horizontal plane. The radius of the circle is 10 cm. If the centripetal force F is kept constant but the angular velocity is halved, the new radius of the path will be ______.
A body of mass m is performing a UCM in a circle of radius r with speed v. The work done by the centripetal force in moving it through `(2/3)`rd of the circular path is ______.
An engine is moving on a c1rcular path of radius 200 m with speed of 15 m/s. What will be the frequency heard by an observer who is at rest at the centre of the circular path, when engine blows the whistle with frequency 250 Hz?
Which of the following statements is FALSE for a particle moving in a circle with a constant angular speed?
A bob is whirled in a horizontal plane by means of a string with an initial speed of ω rpm. The tension in the string is T. If speed becomes 2ω while keeping the same radius, the tension in the string becomes ______.
