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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.
विकल्प
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
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?
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‘θ’ then linear acceleration of body rolling down the plane is _______.
Can an object be in pure translation as well as in pure rotation?
A sphere cannot roll on
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.
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What is the difference between sliding and slipping?
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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 ______.
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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)
