A small object of uniform density rolls up a curved surface with an initial velocity \(v.\) It is reached upto a maximum height of \(\frac{3v^{2}}{4g}\) with respect to the initial position. The object is:

           

1. ring
2. solid sphere
3. hollow sphere
4. disc

Subtopic:  Rolling Motion (OLD NCERT) |
 76%
From NCERT
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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

Subtopic:  Moment of Inertia |
 82%
From NCERT
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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

Subtopic:  Rolling Motion (OLD NCERT) |
From NCERT
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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

Subtopic:  Torque |
 52%
From NCERT
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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

Subtopic:  Angular Momentum |
 51%
From NCERT
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A uniform thin rod is bent in the form of closed loop ABCDEFA as shown in the figure. The ratio of inertia of the loop about x-axis to that about y-axis is:

                        

1.  >1

2.  <1

3.  =1

4.  =1/2

Subtopic:  Moment of Inertia |
 51%
From NCERT
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Four spheres of diameter 2a and mass M are placed with their centres on the four corners of a square of side b. Then the moment of inertia of the system about an axis about one of the sides of the square is

(1) Ma2+2Mb2

(2) Ma2

(3) Ma2+4Mb2

(4) 85Ma2+2Mb2

Subtopic:  Moment of Inertia |
 75%
From NCERT
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A body of mass m slides down an incline and reaches the bottom with a velocity v. If the same mass were in the form of a ring which rolls down this incline, the velocity of the ring at bottom would have been

(1) v

(2)  2 v

(3) 1/2v

(4) 2/5v

Subtopic:  Rolling Motion (OLD NCERT) |
 68%
From NCERT
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A rod is released at an angle 45° to the horizontal as shown. If its length is L, its angular acceleration about its foot at ground is initially

1. 3g2L

2. 3g2L

3. 3g22L

4. 6g2L

Subtopic:  Torque |
 57%
From NCERT
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The moment of inertia of pulley is I and its radius is R. The string doesn't slips on the pulley, as system is released, the acceleration of the system is

(1) g3+ImR2

(2) g1+ImR2

(3) 3g1+ImR2

(4) 3g2+ImR2

Subtopic:  Torque |
 60%
From NCERT
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