Q : 1. Angular momentum of a particle.

(a) Does not depend that about which point it is taken.

(b) Can be zero for a person and non zero for another person.

(c) Is not possible if it is moving in straight line.

(d) Is possible only if it is in circular motion.

Answer Option : (B)

EXPLANATION :
=> We use term "angular momentum" when we study rotational motion. Angular momentum changes if we change the point about which we are calculating angular momentum.
=>Option 2 is correct because, singlequotemotion is relative termsinglequote even it is singlequoteTransitional motion or rotational motionsinglequote.
If a person take angular momentum of mass m (which is moving with constant velocity) about o₁ , it will come out zero and if a another person take angular momentum of same particle about o₂ , it will be " mvr₂ sinθ" (constant).
  
Q : 2 If a rigid body is in rotational motion about a fixed axis.

(a) All the particles of the body move in circular motion.

(b) The relation between is given by  is not correct.

(c) The correct relation between  is .

(d) The direction of  is taken by convention.

Answer Option : (D)

EXPLANATION :
The particles on the axis will not move.
The relation between can be   because it depends that what direction you choose for  (as you choose direction of by convention).

Q : 3. Moment of inertia of the two rod
System about the axis passing through A and perpendicular to the plane of system.

(a) 5/12 Ml²

(b) Ml² /6

(c) 2Ml² /3

(d) Ml² /12

Answer Option : (A)

EXPLANATION :
=>
=> Moment of inertia is a scalar quantity, so first you can find the moment of inertia of the two rods separately and just add them.
=> Moment of inertia of (1) rod about center o = Ml²/12.
=>Moment of inertia of (1) rod about A =  Ml²/12 + Ml²/4 = Ml³/3 .
=>Moment of (2) rod about A = Ml²/3
=>So, Moment of system = Ml²/3 + Ml²/3
                                         = 2/3 ml² .

Q : 4. The relation between moment of inertia of the disc and ring of same mass and same radius.

(a) Moment of inertia ring must be greater than the momentum of inertia of disc.

(b) Moment of inertia of disc must be greater than the moment of inertia of ring.

(c) Moment of inertia of ring may be greater than the moment of inertia of disc.

(d) Moment of inertia of disc may be greater than the Moment of inertia of ring.

Answer Option : (C), (D)

EXPLANATION :
=> you may think that Moment of inertia of ring is MR² , and Moment of inertia of disc is MR²/2, but keep in mind that these Moment of inertia for ring and disc is about axis which pass through geometrical center and perpendicular to their plane.
=>Means Moment of inertia also depend on that about which axis you want to know Moment of inertia of the body.
=> By example

Here I₂ > I₁ .

Q : 5.
In the above diagram a force is applied on string which is wrapped on an object which will rotate as string will go down (means string will not slip on the object). so relation between the acceleration of the string and angular acceleration of rotating object is-

(a) Must equal to .

(b) Must be less than.

(c) May be equal to.

(d) Depends on the rotating object.

Answer Option : (B), (D)

EXPLANATION :




Q : 6.
A rod with uniform mass distribution is kept at rest as shown the figure.

(a) Above situation is not possible if μ = 0 between rod and wall.

(b) Above situation is possible if the μ 0 between floor and rod₁ condition in part (1) does not matter.

(c) If there is no friction any where still rod can be at rest.

(d) Option 1 and 3 both are wrong.

Answer Option : (B), (D)

EXPLANATION :


Rod will remain in equilibrium, if floor has some friction, otherwise

=> So for the rod to be in equilibrium
f s = N₂  .

Q : 7

As shown in the figure a ball hits a rod AB and stop. Rod was initially at rest on a friction less horizontal table.

(a) It will only rotate about end A.

(b) It will only rotate about point o.

(c) It will rotate as well as translate ahead.

(d) Velocity of point o will show translation motion of the rod.

Answer Option : (C), (D)

EXPLANATION : From conservation of angular momentum and conservation of linear momentum you can observe the correct options.

Q : 8. A wheel is rotating about an axle at an angular speed of 20 radian/sec. The friction at the axle is zero.

If bring another identical wheel- axle system and touch it to the first wheel  (which is rotating at an angular speed of 20 radian/sec.).

(a) The angular momentum of both the wheels have same value after same time.

(b) The magnitude of the angular momentum of both the wheel have same value after some time.

(c) The net angular momentum of the two wheels system is same before and after the touch.

(d) Option 1 and 3 are the correct option.

Answer Option : (B), (C)

EXPLANATION :


The magnitude of angular momentum of both will be same.
=> The total angular momentum of the system will remain in conserved because the net external torque and net external force on the system is zero.

Q : 9.