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
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
2 : 1
√5 : √6
1 : √2
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
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
1 : 1
The moment of inertia of a body about a given axis is 1.2 kg – m2. 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
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 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 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
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
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
