A solid cylinder of mass M and radius R rolls down an inclined plane of height h without slipping. The speed of its centre of mass when it reaches the bottom is
√2gh
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 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 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
The moment of inertia of a disc of mass M and radius R about a tangent to its rim in its plane is
2/3 MR2
3/2 MR2
4/5 MR2
5/4 MR2
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
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 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
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
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
