A cylinder of mass M_{c} and sphere of mass M_{s} are placed at points A and B of two inclines, respectively.
(See Figure). If they roll on the incline without slipping such that their accelerations are the same, then
The ratio is
When a steady torque is acting on a body, the body
Continues in its state of rest or uniform motion along a straight line
Gets linear acceleration
Gets angular acceleration
Rotates at a constant speed
When a mass is rotating in a plane about a fixed point its angular momentum is directed along.
The radius
The tangent to orbit
The line at an angle of 45° to the plane of rotation
The axis of rotation
Two disc with same mass but different radii are moving with same K.E. One of them rolls and other slides without friction. Then
Rolling disc has greater velocity
Sliding disc has greater velocity
Both have same velocity
The disc with greater radius will have greater velocity
The torque acting is 2000 Nm with an angular acceleration of 2 rad/. The moment of inertia of body is
1200 kg
900 kg
1000 kg
Can't say
The term moment of momentum is called
Momentum
Force
Torque
Angular Momentum
The speed of a homogeneous, solid sphere after rolling down in the inclined plane of vertical height h, from rest without sliding is
The moment of inertia of a circular ring about an axis passing through its centre and normal to its plane is 200 gm , then its moment of inertia about a diameter is
400 gm
300 gm
200 gm
100 gm
The moment of inertia of a body comes into play
In motion along a curved path
In linear motion
In rotational motion
None of the above
The M.I. of a solid cylinder of mass M and radius R about a line parallel to the axis of the cylinder and ling on the surface of the cylinder is
If I, a and t are the moment of inertia, angular acceleration and torque respectively of a body rotating about any axis with angular velocity w, then
t = Ia
t = Iw
I = tw
a = Iw
By keeping moment of inertia of a body is constant, if we double the time period, then angular momentum of body is
Remains constant
Doubles
Becomes half
Quadruples
As we learnt in
Law of conservation of angular moment -
- wherein
If net torque is zero
i.e.
angular momentum is conserved only when external torque is zero .
Becomes half.
Option 1)
Remains constant
Incorrect
Option 2)
Doubles
Incorrect
Option 3)
Becomes half
Correct
Option 4)
Quadruples
Incorrect
A wheel of mass 2 kg having practically all the mass concentrated along the circumference of a circle of radius 20 cm, is rotating on its axis with an angular velocity of 100 rad/s. The rotational kinetic energy of the wheel is
4 J
70 J
400 J
800 J
A uniform solid circular cylinder of radius r is placed on a rough horizontal surface and given a linear velocity and angular velocity as shown in the figure. The speed of cylinder when it starts rolling
5/2
3/2
5/3
2/3
The moment of inertia of a disc about its geometrical axis is I. then its M.I. about its diameter will be
I
2I
A uniform disc of mass 2 kg is rotated about an axis perpendicular to the plane of the disc. If radius of gyration is 50 cm, then the M.I. of disc about same axis is
0.25 kg
0.5 kg
2 kg
1 kg
A uniform circular disc of radius r is placed on a rough horizontal surface and given a linear velocity v_{o} and angular velocity as shown. The disc comes to rest after moving some distance to the right. It follows that
A thin uniform, circular ring is rolling down an inclined plane of inclination 30° without slipping. Its linear acceleration along the inclined plane will be
g/2
g/3
g/4
2g/3
A thin hollow sphere of mass m is completely filled with an ideal liquid of mass m. When the sphere rolls with a velocity v kinetic energy of the system is equal to
(1/2)
(4/3)
(4/5)
A thin circular ring of mass M and radius R is rotating about its axis with a constant angular velocity ω . Two objects, each of mass m are attached gently to the opposite ends of the diameter of the ring. The wheel now rotates with an angular velocity.
ω M/(M + m)
{(M – 2m)/(M +2m)}ω
{M/(M + 2m)}ω
{(M + 2m)/M} ω