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प्रश्न
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?
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उत्तर
Let the acceleration of the centre of mass of the disc be ‘a’, then
`Ma = F - f` ......(1)
The angular acceleration of the disc is `α = a/R`. (if there is no sliding).
Then `(1/2 MR^2)α = Rf` ......(2)
⇒ `Ma = 2f`
Thus, `f = F/3`. Since there is no sliding,
⇒ `f ≤ µmg`
⇒ `F ≤ 3µMg`.
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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.
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;
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A sphere cannot roll on
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, _____________ .
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.
What is the condition for pure rolling?
Discuss rolling on an inclined plane and arrive at the expression for acceleration.
A solid spherical ball rolls on an inclined plane without slipping. The ratio of rotational energy and total energy is ______.
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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)
