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
0.5 ms –2
Referring to fig, the cyclist is moving on a straight road from A to B with a velocity v = 6 ms–1.
As he approaches the circular turn, he decelerates at rate at, represented by vector BD. The magnitude of declaration is At point B, two accelerations at and ac, the centripetal acceleration directed towards the centre C act on the cyclist. Using the law of parallelogram of vector addition, vector BE gives the resultant acceleration a whose magnitude is
A disc, initially at rest, is rotated about its axis with a uniform angular acceleration. In the first two seconds, it rotates through an angle θ. In the next two seconds, the disc will rotate through an angle
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 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:
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:
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
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
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.