Two racing cars of masses m and 4m are moving in circles of radii r and 2r respectively. If their speeds are such that each makes a complete circle in the same time. Then the ratio of the angular speeds of the first to the second car is
8 : 1
4 : 1
2 : 1
1 : 1
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 solid sphere and a hollow sphere are thrown horizontally from a cliff with equal velocities, respectively. Then which sphere reaches first on earth ?
Solid sphere
Hollow sphere
Both sphere simultaneously
We cannot say because masses of spheres are not given
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 center of mass is conserved
Angular momentum about the center of mass is conserved
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 = 5 m
x = 0
A thin uniform circular ring is rolling down an inclined plane of inclination 30o without slipping. Its linear acceleration along the inclined plane will be :
g/2
g/3
g/4
2g/3
A ball of mass 0.25 kg attached to the end of a string of length 1.96 m is moving in a horizontal circle. The string will break if the tension is more than 25 N. What is the maximum speed with which the ball can be moved ?
14 m/s
3 m/s
3.92 m/s
5 m/s
Moment of inertia of a uniform circular disc about a diameter is I. Its moment of inertia about an axis perpendicular to its plane and passing trough a point on its rim will be
5 I
3 I
6 I
4 I
If a sphere is rolling, the ratio of the translational energy to total kinetic energy is given by
7 : 10
2 : 5
10 : 7
5 : 7
At any instant, a rolling body may be considered to be in pure rotation about an axis trough the point of contact. This axis is translating forward with speed .
Equal to center of mass
Zero
Twice of center of mass
Data is insufficient