Question

One end of a string of length R is tied to a stone of mass m and the other end to a small pivot on a frictionless vertical board. The stone is whirled in a vertical circle with the pivot as the centre. The minimum speed the stone must have, when it is at the topmost point on the circle, so that the string does not slack is given by

Solution

Correct option is

 

Referring to fig, when the stone is at the topmost point A, the net force towards the centre is

                                                …(i)

When the stone is at the lowermost point B, the net force towards the centre is  

                                                 …(ii)

The relation between vA and vB can be obtained from the principle of conservation of energy. Let the gravitational potential energy be zero at the lowermost point B. Then

                       

  

                                        

Now, when the stone is at A, the

 string will not stack if the whole

of centripetal force is provided by

the weight mg,

                   

SIMILAR QUESTIONS

Q1

A string can withstand a tension of 25 N. What is the greatest speed at which a body of mass 1 kg can be whirled in a horizontal circle using a 1 m length of a string?

Q2

A body of mass 0.5 kg is whirled in a vertical circle at an angular frequency of 10 rad s–1. If the radius of the circle is 0.5 m, what is the tension in the string when the body is at the top of the circle? Take g = 10 ms–2.

Q3

A stone, tied to the end of a string of length 50 cm, is whirled in a horizontal circle with a constant speed. If the stone makes 40 revolutions in 20 s, what is the speed of the stone along the circle?

Q4

A cyclist is moving with a speed of 6 ms–1. As he approaches a circular turn on the road of radius 120 m, he applies brakes and reduces his speed at a constant rate of 0.4 ms–2. The magnitude of the net acceleration of the cyclist on the circular turn is 

Q5

 

A simple pendulum of length L and with a bob of mass M is oscillating in a plane about a vertical line between angular limits

–Ï• and +Ï•. For an angular displacement θ (< Ï•) the tension is the string and the velocity of the bob are T and v respectively. The flowing relations hold good under the above conditions:

Q6

A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle. The motion of the particle takes place in a plane. It follows that:

Q7

A simple pendulum of bob mass m swings with an angular amplitude of 40o. When its angular displacement is 20o, the tension in the string is

Q8

A car moves at a speed of 36 km h–1 on a level road. The coefficient of friction between the tyres and the road is 0.8. The car negotiates a curve of radius R. If g = 10 ms –2, the car will skid (or slip) while negotiating the curve if value of R is  

Q9

 

A train has to negotiate a curve of radius 200 m. by how much should the outer rails be raised with respect to the inner rails for a speed of 36 km h –1. The distance between the rails is 1.5 m.

Take g = 10 ms–2

Q10

The pilot of an aircraft, who is not tied to his seat, can loop a vertical circle in air without falling out at the top of the loop. What is the minimum speed required so that he can successfully negotiate a loop or radius 4 km? Take g = 10 ms–2