Advertisements
Advertisements
प्रश्न
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, ___________ .
पर्याय
the heavier sphere reaches the bottom first
the bigger sphere reaches the bottom first
the two spheres reach the bottom together
the information given is not sufficient to tell which sphere will reach the bottom first
उत्तर
the two spheres reach the bottom together
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 \[= \frac{2}{5}m r^2 \]
\[So, a = \frac{g\sin\theta}{1 + \frac{2m r^2}{5m r^2}} = \frac{5}{7}g\sin\theta\]
a is independent of mass and radii; therefore, the two spheres reach the bottom together.
APPEARS IN
संबंधित प्रश्न
Derive an expression for kinetic energy, when a rigid body is rolling on a horizontal surface without slipping. Hence find kinetic energy for a solid sphere.
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.
A sphere cannot roll on
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.
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 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 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 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).
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.
The speed of a solid sphere after rolling down from rest without sliding on an inclined plane of vertical height h is, ______
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 solid spherical ball rolls on an inclined plane without slipping. The ratio of rotational energy and total energy 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 ______.
The angular displacement of a particle in 6 sec on a circle with angular velocity `pi/3` rad/sec is ______.
