If I is the moment of inertia of a solid sphere about an axisparallel to a diameter of sphere and at a distance x from it.Which of the following graph represents the variation of Iwith x?

Concept Questions :-

Moment of inertia
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A particle is rotating under the central force, in which one of the following quantities is constant:

1.  torque

2.  angular momentum

3.  linear momentum

4.  none of these

Concept Questions :-

Angular momentum
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A small object of uniform density rolls up a curved surface with an initial velocity v. It is reached upto a maximum height of 3v24g w.r.t. the initial position. The object is:

            

1.  Ring

2.  Solid sphere

3.  Hollow sphere

4.  Disc

Concept Questions :-

Rolling motion
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A point is at (x, y, z). What is its moment of inertia about x-axis:

                          

1.  mx2+y2+z2

2.  mx2+y2

3.  my2+z2

4.  mx2+z2

Concept Questions :-

Moment of inertia
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What minimum friction coefficient is required for hollow sphere rolling without slipping on the inclined plane with an angle of inclination 37° ?

1.  310

2.  314

3.  316

4.  None of these

Concept Questions :-

Rolling motion
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The disc is placed on the rough horizontal surface given only angular velocity ω0. The velocity of the centre of mass when it starts pure rolling is:

1.  ω0R2

2.  ω0R3

3.  ω0R4

4.  ω0R6

Concept Questions :-

Rolling motion
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A force 2N is along line y = 3x + 4. The torque about the origin is:

1.  510Nm

2.  710Nm

3.  610Nm

4.  810Nm

Concept Questions :-

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A uniform bar of length 6a and mass 8m lies on a smooth horizontal table. Two-point
masses m and 2m moving in the same horizontal plane with speeds 2v and v
respectively strike the bar as shown below in the figure and stick to the bar after the collision. Denoting angular velocity about the center of mass, total energy, and center of mass velocity of ω, E and vc respectively, we have after collision

                      

1.  vc = 2 m/s 

2.  ω = 35va

3.  ω = v5a 

4.  E = 23 mv2

Concept Questions :-

Angular momentum
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A stone is projected from a horizontal plane. It attains maximum height 'H' & strikes a stationary smooth wall & falls on the ground vertically below the maximum height. Assume the collision to be elastic, the height of the point on the wall where ball will strike is:

(1) H2

(2) H4

(3) 3H4

(4) None of these

Concept Questions :-

Linear momentum
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A train of mass M is moving on a circular track of radius 'R' with constant speed v. The length of the train is half of the perimeter of the track. The linear momentum of the train will be 

1. 0

2. 2Mvπ

3. MvR

4. Mv

Concept Questions :-

Linear momentum
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