In the figure shown, a small solid spherical ball of mass 'm' can move without sliding in a fixed semicircular track of radius R in vertical plane. It is released from the top. The resultant force on the ball at the lowest point of the track is :

1. 10 mg 7

2. 17 mg 7

3. 3 mg 7

4. zero

Concept Questions :-

Rolling motion
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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

Concept Questions :-

Moment of inertia
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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

Concept Questions :-

Moment of inertia
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A body of mass (m) elastically collides with another stationary body of mass 3m. The fractional loss of K.E. of the body is:

1.  89

2.  34

3.  35

4.  47

Concept Questions :-

Linear momentum
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A hollow sphere is rolling without slipping on the inclined plane. The minimum coefficient of friction is :

1. 25tanθ

2. 23tanθ

3. 34tanθ

4. 57tanθ

Concept Questions :-

Rolling motion
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A body of mass (m) is projected with velocity v0 at an angle of projection θ. The magnitude of angular momentum about origin after time t from projection is :

1. Increase with time

2. decrease with time

3. independent of time

4. none of these

Concept Questions :-

Angular momentum
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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

Concept Questions :-

Rolling motion
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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

Concept Questions :-

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From a disc of mass M and radius '2a', a concentric disc of radius 'a' is cut out. The moment of inertia of remaining disc is 

1.  Ma28  

2.  1516Ma2  

3.  78Ma2  

4.  32Ma2

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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

Concept Questions :-

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