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
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 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 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
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
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
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
