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प्रश्न
A hollow sphere and a solid sphere having same mss and same radii are rolled down a rough inclined plane.
पर्याय
The hollow sphere reaches the bottom first.
The solid sphere reaches the bottom with greater speed
The solid sphere reaches the bottom with greater kinetic energy.
The two spheres will reach the bottom with same linear momentum.
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उत्तर
The solid sphere reaches the bottom with greater speed.
Acceleration of a sphere on the incline plane is given by
\[a = \frac{g\sin\theta}{1 + \frac{I_{COM}}{m r^2}}\]
\[ I_{COM}\] for a solid sphere \[= \frac{2}{5}m r^2 \]
\[\text{So, }a = \frac{g\sin\theta}{1 + \frac{2m r^2}{5m r^2}} = \frac{5}{7}g\sin\theta\]
\[I_{COM}\] for a hollow sphere \[= \frac{2}{3}m r^2 \]
\[\text{So, }a' = \frac{g\sin\theta}{1 + \frac{2m r^2}{3m r^2}} = \frac{3}{5}g\sin\theta\]
The acceleration of the solid sphere is greater; therefore, it will reach the bottom with greater speed.
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संबंधित 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
Two uniform solid spheres having unequal masses and unequal radii are released from rest from the same height on a rough incline. If the spheres roll without slipping, ___________ .
In rear-wheel drive cars, the engine rotates the rear wheels and the front wheels rotate only because the car moves. If such a car accelerates on a horizontal road the friction
(a) on the rear wheels is in the forward direction
(b) on the front wheels is in the backward direction
(c) on the rear wheels has larger magnitude than the friction on the front wheels
(d) on the car is in the backward direction.
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, _____________ .
A cylinder rolls on a horizontal place surface. If the speed of the centre is 25 m/s, what is the speed of the highest point?
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).
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?
What is the difference between sliding and slipping?
Discuss rolling on an inclined plane and arrive at the expression for acceleration.
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)
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 ____________.
A ring and a disc roll on horizontal surface without slipping with same linear velocity. If both have same mass and total kinetic energy of the ring is 4 J then total kinetic energy of the disc is ______.
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 ______.
When a sphere rolls without slipping, the ratio of its kinetic energy of translation to its total kinetic energy is ______.
