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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, _____________ .
विकल्प
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
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.
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 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)
A sphere cannot roll on
The following figure shows a smooth inclined plane fixed in a car accelerating on a horizontal road. The angle of incline θ is related to the acceleration a of the car as a = g tanθ. If the sphere is set in pure rolling on the incline, _____________.
A string is wrapped over the edge of a uniform disc and the free end is fixed with the ceiling. The disc moves down, unwinding the string. Find the downward acceleration of the disc.
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?
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.
A pendulum consisting of a massless string of length 20 cm and a tiny bob of mass 100 g is set up as a conical pendulum. Its bob now performs 75 rpm. Calculate kinetic energy and increase in the gravitational potential energy of the bob. (Use π2 = 10)
The speed of a solid sphere after rolling down from rest without sliding on an inclined plane of vertical height h 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 angular velocity of minute hand of a clock in degree per second is ______.
A uniform disc of radius R, is resting on a table on its rim.The coefficient of friction between disc and table is µ (Figure). Now the disc is pulled with a force F as shown in the figure. What is the maximum value of F for which the disc rolls without slipping?
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 ______.
The least coefficient of friction for an inclined plane inclined at angle α with horizontal in order that a solid cylinder will roll down without slipping 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)
The kinetic energy and angular momentum of a body rotating with constant angular velocity are E and L. What does `(2E)/L` represent?
When a sphere rolls without slipping, the ratio of its kinetic energy of translation to its total kinetic energy is ______.
An inclined plane makes an angle 30° with the horizontal. A solid sphere rolling down an inclined plane from rest without slipping has linear acceleration ______. (g = acceleration due gravity) (sin 30° = 0.5)
