Advertisements
Advertisements
प्रश्न
In the previous question, the smallest kinetic energy at
the bottom of the incline will be achieved by ___________ .
पर्याय
the solid sphere
the hollow sphere
the disc
all will achieve same kinetic energy
Advertisements
उत्तर
the hollow sphere
Torque is same for all the bodies; therefore, the angular momentum will be conserved.
Now, total kinetic energy = \[\frac{1}{2}m v^2 + \frac{L^2}{2I}\]
So, the body with greater value of moment of inertia will have smallest kinetic energy at the bottom of the incline.
Order of the moment of inertia of the bodies:-
hollow sphere > disc > solid sphere
Hence, the hollow sphere will have the smallest kinetic energy at the bottom.
APPEARS IN
संबंधित प्रश्न
If the ice at the poles melts and flows towards the equator, how will it affect the duration of day-night?
A hollow sphere, a solid sphere, a disc and a ring all having same mass and radius are rolled down on an inclined plane. If no slipping takes place, which one will take the smallest time to cover a given length?
A closed cylindrical tube containing some water (not filling the entire tube) lies in a horizontal plane. If the tube is rotated about a perpendicular bisector, the moment of inertia of water about the axis __________ .
A cubical block of mass M and edge a slides down a rough inclined plane of inclination θ with a uniform velocity. The torque of the normal force on the block about its centre has a magnitude
The centre of a wheel rolling on a plane surface moves with a speed \[\nu_0\] A particle on the rim of the wheel at the same level as the centre will be moving at speed ___________ .
A solid sphere, a hollow sphere and a disc, all having same mass and radius, are placed at the top of a smooth incline and released. Least time will be taken in reaching the bottom by _________ .
A solid sphere, a hollow sphere and a disc, all having same mass and radius, are placed at the top on an incline and released. The friction coefficients between the objects and the incline are same and not sufficient to allow pure rolling. Least time will be taken in reaching the bottom by ___________ .
A string of negligible thickness is wrapped several times around a cylinder kept on a rough horizontal surface. A man standing at a distance l from the cylinder holds one end of the string and pulls the cylinder towards him (see the following figure). There is no slipping anywhere. The length of the string passed through the hand of the man while the cylinder reaches his hands is _________ .
Consider a wheel of a bicycle rolling on a level road at a linear speed \[\nu_0\] (see the following figure)
(a) the speed of the particle A is zero
(b) the speed of B, C and D are all equal to \[v_0\]
(c) the speed of C is 2 \[v_0\]
(d) the speed of B is greater than the speed of O.
Three particles, each of mass 200 g, are kept at the corners of an equilateral triangle of side 10 cm. Find the moment of inertial of the system about an axis joining two of the particles.
Particles of masses 1 g, 2 g, 3 g, .........., 100 g are kept at the marks 1 cm, 2 cm, 3 cm, ..........., 100 cm respectively on a metre scale. Find the moment of inertia of the system of particles about a perpendicular bisector of the metre scale.
Find the moment of inertia of a pair of spheres, each having a mass mass m and radius r, kept in contact about the tangent passing through the point of contact.
The moment of inertia of a uniform rod of mass 0⋅50 kg and length 1 m is 0⋅10 kg-m2about a line perpendicular to the rod. Find the distance of this line from the middle point of the rod.
The radius of gyration of a uniform disc about a line perpendicular to the disc equals its radius. Find the distance of the line from the centre.
Suppose the rod in the previous problem has a mass of 1 kg distributed uniformly over its length.
(a) Find the initial angular acceleration of the rod.
(b) Find the tension in the supports to the blocks of mass 2 kg and 5 kg.
The following figure shows two blocks of mass m and M connected by a string passing over a pulley. The horizontal table over which the mass m slides is smooth. The pulley has a radius r and moment of inertia I about its axis and it can freely rotate about this axis. Find the acceleration of the mass M assuming that the string does not slip on the pulley.
A small spherical ball is released from a point at a height h on a rough track shown in the following figure. Assuming that it does not slip anywhere, find its linear speed when it rolls on the horizontal part of the track.
