A solid homogenous sphere of mass M and radius R is moving on a rough horizontal surface, party rolling and party sliding during this kind of motion of the sphere ?
Total Kinetic energy is conserved
The angular momentum of the sphere about the point of contact with the plane is conserved
Only the rotational kinetic energy about the centre of mass is conserved
Angular momentum about the centre of mass is conserved
In a carbon monoxide molecule, the carbon and the oxygen atoms are separated by a distance 1.12 x 10 -10 m. The distance of the centre of mass form the carbon atom is _____.
0.64 x 10 -10 m
0.56 x 10 -10 m
0.51 x 10 -10 m
0.48 x 10 -10 m
A cart of mass M is tied to one end of a massless rope of length 10 m. The other end of the rope is in the hands of a man of mass M. The entire system is on a smooth horizontal surface. The man is at x = 0 and the car at x = 10 m. If the man pulls the cart by the rope, the man and the cart will meet at the point.
they will never meet
x = 10 m
x = 5m
x = 0
A particle of mass M is revolving along a circle of radius R and another particle of mass m is revolving in a circle of radius r. If time periods of both particles are same, then the ratio of their angular velocities is
1
R/r
r/R
A ball rolls without slipping. The radius of gyration of the ball about an axis passing through its centre of mass is k. If radius of the ball be R, then the fraction of total energy associated with its rotational energy will be
Four identical thin rods each of mass M and length l, form a square frame. Moment of inertia of this frame about an axis through the centre of the square and perpendicular to its plane is
4/3 Ml2
2/3 Ml2
13/3 Ml2
1/3 Ml2
The moment of inertia of a body about a given axis is 1.2 kgm2. Initially, the body is at rest, in order to produce a rotational kinetic energy of 1500 J, an angular acceleration of 25 rad/s2 must be applied about that axis for a duration of :
4 s
2 s
8 s
10 s
Two bodies have their moments of inertia I and 2 I respectively about their axis of rotation. If their kinetic energies of rotation are equal, their angular momenta will be in the ratio
1 : 2
√2 : 1
2 : 1
1 : √2
If a flywheel makes 120 rev/min, then its angular speed will be
8 π rad/s
6 π rad/s
4 π rad/s
2 π rad/s
A solid sphere, disc and solid cylinder, all of the same mass and made of same material are allowed to roll down ( from rest ) on the inclined plane, then :
Solid sphere reaches the bottom first
Solid sphere reaches the bottom last
Disc will reach the bottom first
All reach the bottom at the same time
