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 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
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
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 round disc of moment of inertia I2 about its axis perpendicular to its plane and passing through its center is placed over another disc of moment of inertia I1 rotating with an angular velocity ω about the same axis. The final angular velocity of the combination of discs is
ω
If a fly wheel 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 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
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
A spherical ball rolls on a table without slipping. Then the fraction of its total energy associated with rotation is
2/5
2/7
3/5
3/7
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
