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प्रश्न
A sphere can roll on a surface inclined at an angle θ if the friction coefficient is more than \[\frac{2}{7}g \tan\theta.\] Suppose the friction coefficient is \[\frac{1}{7}g\ tan\theta.\] If a sphere is released from rest on the incline, _____________ .
पर्याय
it will stay at rest
it will make pure translational motion
it will translate and rotate about the centre
the angular momentum of the sphere about its centre will remain constant
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उत्तर
it will translate and rotate about the centre
The given coefficient of friction \[\left(\frac{1}{7}g\ tan\theta\right)\] is less than the coefficient friction \[\left(\frac{2}{7}g\ tan\theta\right)\] required for perfect rolling of the sphere on the inclined plane.
Therefore, sphere may slip while rolling and it will translate and rotate about the centre.
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संबंधित प्रश्न
A solid sphere rolls down two different inclined planes of the same heights but different angles of inclination. (a) Will it reach the bottom with the same speed in each case? (b) Will it take longer to roll down one plane than the other? (c) If so, which one and why?
Read each statement below carefully, and state, with reasons, if it is true or false;
For perfect rolling motion, work done against friction is zero.
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
If a rigid body of radius ‘R’ starts from rest and rolls down an inclined plane of inclination
‘θ’ then linear acceleration of body rolling down the plane is _______.
A solid sphere of mass 0⋅50 kg is kept on a horizontal surface. The coefficient of static friction between the surfaces in contact is 2/7. What maximum force can be applied at the highest point in the horizontal direction so that the sphere does not slip on the surface?
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.
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 of mass 1 kg and radius 10 cm rolls without slipping on a horizontal surface, with velocity of 10 emfs. The total kinetic energy of sphere is ______.
A man is supported on a frictionless horizontal surface. It is attached to a string and rotates about a fixed centre at an angular velocity `omega`. The tension in the strings is F. If the length of string and angular velocity are doubled, the tension in string is now ____________.
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 ______.
The angular velocity of minute hand of a clock in degree per second is ______.
Solid spherical ball is rolling on a frictionless horizontal plane surface about is axis of symmetry. The ratio of rotational kinetic energy of the ball to its total kinetic energy is ______.
If x = at + bt2, where x is the distance travelled by the body in kilometers while t is the time in seconds, then the unit of b is ______.
A solid sphere of mass 2 kg is rolling on a frictionless horizontal surface with velocity 6m/s. It collides on the free end of an ideal spring whose other end is fixed. The maximum compression produced in the spring will be ______.
(Force constant of the spring = 36 N/m)
When a sphere rolls without slipping, the ratio of its kinetic energy of translation to its total kinetic energy is ______.
