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.
Radius of the curve (R) = 200 m
Distance between rails (x) = 1.5 m
Let the outer rails be raised by a height h with respect to the inner rails so that the angle of banking is θ (fig.)
A body moves along a circular track of radius 20 cm. It starts from one end of a diameter, moves along the circular track and reaches the other end of the diameter is 5 seconds. What is the angular speed of the body?
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?
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.
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?
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
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–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:
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:
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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