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
ABC is a right angled triangular plate of uniform thickness. The sides are such that AB > BC as shown in figure. I1 , I2, I3 are moments of inertia about AB, BC and AC respectively. Then which of the following relations is correct ?
I1 = I2 = I3
I2 > I1 > I3
I3 < I2 < I1
I3 > I1 > I2
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
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
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 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
The ratio of the radii of gyration of a circular disc about a tangential axis in the plane of the disc and of a circular ring of the same radius about a tangential axis in the plane of the ring is
2 : 3
√5 : √6
1 : √2
The angular speed of an engine wheel making 90 rev/min is
1.5 π rad/s
3 π rad/s
4.5 π rad/s
6 π rad/s
If a fly wheel makes 120 rev/min, then its angular speed will be
8 π rad/s
4 π rad/s
2 π rad/s
A couple produces
No motion
Linear and rotational motion
Purely rotational motion
Purely linear motion
