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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In uniform circular motion

(1) Both the angular velocity and the angular momentum vary

(2) The angular velocity varies but the angular momentum remains constant

(3) Both the angular velocity and the angular momentum stay constant

(4) The angular momentum varies but the angular velocity remains constant

Subtopic:  Angular Momentum |
From NCERT
PMT - 1994
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A wheel is subjected to uniform angular acceleration about its axis. Initially, its angular velocity is zero. In the first 2 sec, it rotates through an angle θ1. In the next 2 seconds, it rotates through an additional angle θ2. The ratio of θ21 is: 

1. 1 2. 2
3. 3 4. 5
Subtopic:  Rotational Motion: Kinematics |
 61%
From NCERT
AIIMS - 1985
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A particle of mass m moving with velocity u makes an elastic one-dimensional collision with a stationary particle of mass m. They are in contact for a very short time T. Their force of interaction increases from zero to F0 linearly in time T/2 and decreases linearly to zero in further time T/2. The magnitude of F0 is:

(1) mu/T

(2) 2mu/T

(3) mu/2T

(4) None of these

Subtopic:  Linear Momentum |
 75%
From NCERT
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A force of 50 dynes is acted on a body of mass 5 g which acts for an interval of 3 seconds, then impulse is 

(1) 0.15 × 10–3 N-s

(2) 0.98 × 10–3 N-s

(3) 1.5 × 10–3 N-s

(4) 2.5 × 10–3 N-s

Subtopic:  Linear Momentum |
 78%
From NCERT
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