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प्रश्न
Read each statement below carefully, and state, with reasons, if it is true or false;
A wheel moving down a perfectly frictionless inclined plane will undergo slipping (not rolling) motion
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उत्तर
True
The rolling of a body occurs when a frictional force acts between the body and the surface. This frictional force provides the torque necessary for rolling. In the absence of a frictional force, the body slips from the inclined plane under the effect of its own weight.
संबंधित प्रश्न
Prove the result that the velocity v of translation of a rolling body (like a ring, disc, cylinder or sphere) at the bottom of an inclined plane of a height h is given by `v^2 = (2gh)/((1+k^2"/"R^2))`.
Using dynamical consideration (i.e. by consideration of forces and torques). Note k is the radius of gyration of the body about its symmetry axis, and R is the radius of the body. The body starts from rest at the top of the plane.
Read each statement below carefully, and state, with reasons, if it is true or false;
The instantaneous speed of the point of contact during rolling is zero.
A stone of mass 2 kg is whirled in a horizontal circle attached at the end of 1.5m long string. If the string makes an angle of 30° with vertical, compute its period. (g = 9.8 m/s2)
Can an object be in pure translation as well as in pure rotation?
A sphere cannot roll on
A hollow sphere is released from the top of an inclined plane of inclination θ. (a) What should be the minimum coefficient of friction between the sphere and the plane to prevent sliding? (b) Find the kinetic energy of the ball as it moves down a length l on the incline if the friction coefficient is half the value calculated in part (a).
Discuss the interlink between translational, rotational and total kinetic energies of a rigid object rolls without slipping.
Answer in Brief:
A rigid object is rolling down an inclined plane derive the expression for the acceleration along the track and the speed after falling through a certain vertical distance.
The speed of a solid sphere after rolling down from rest without sliding on an inclined plane of vertical height h is, ______
Discuss rolling on an inclined plane and arrive at the expression for acceleration.
A uniform disc of mass 100g has a diameter of 10 cm. Calculate the total energy of the disc when rolling along with a horizontal table with a velocity of 20 cms-1. (take the surface of the table as reference)
A solid sphere rolls down from top of inclined plane, 7m high, without slipping. Its linear speed at the foot of plane is ______. (g = 10 m/s2)
The power (P) is supplied to rotating body having moment of inertia 'I' and angular acceleration 'α'. Its instantaneous angular velocity is ______.
A solid sphere is rolling on a frictionless surface with translational velocity 'V'. It climbs the inclined plane from 'A' to 'B' and then moves away from Bon the smooth horizontal surface. The value of 'V' should be ______.
A 1000 kg car has four 10 kg wheels. When the car is moving, fraction of total K.E. of the car due to rotation of the wheels about their axles is nearly (Assume wheels be uniform disc)
An object is rolling without slipping on a horizontal surface and its rotational kinetic energy is two-thirds of translational kinetic energy. The body is ______.
A solid spherical ball rolls on an inclined plane without slipping. The ratio of rotational energy and total energy is ______.
The kinetic energy and angular momentum of a body rotating with constant angular velocity are E and L. What does `(2E)/L` represent?
The angular displacement of a particle in 6 sec on a circle with angular velocity `pi/3` rad/sec is ______.
When a sphere rolls without slipping, the ratio of its kinetic energy of translation to its total kinetic energy is ______.
