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Question (1)

QN0038689

For which of the following does the centre of mass lie outside the body?

(A)
A pencil
(B)
A shotput
(C)
A dice
(D)
A bangle

Correct Answer: D

Explanation:

A bangle is in the form of a ring as shown in figure. The centre of mass of the ring lies at its centre, which is outside the ring or bangle.

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Question (2)

QN0038690

Which of the following points is the likely position of the centre of mass of the system shown in figure?

(A)
A
(B)
B
(C)
C
(D)
D

Correct Answer: C

Explanation:

Centre of mass of a system lies towards the part of the system, having bigger mass. In the above diagram, lower part is heavier, hence of the system lies below the horizontal diameter at point.

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Question (3)

QN0038691

A particle of mass is moving in -plane with a uniform velocity with its trajectory running parallel to tve -axis and intersecting -axis at in figure. The change in its angular momentum about the origin as it bounces elastically from a wall at constant is

(A)
(B)
(C)
(D)

Correct Answer: B

Explanation:

The initial velocity is and after reflection from the wall, the final velocity is . The trajectory is at constant distance on axis and as particle moves along axis, its component changes .

So position vector (moving along -axis),

Hence, the change in angular momentum is .

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Question (4)

QN0038692

When a disc rotates with uniform angular velocity, which of following is not true?

(A)
The sense of rotation remains same
(B)
The orientation of the axis of rotation remains same
(C)
The speed of rotation is non-zero and remains same
(D)
The angular acceleration is non-zero and remains same

Correct Answer: D

Explanation:

Angular acceleration where is angular velocity of the disc and is uniform or constant.

Hence, angular acceleration is zero:

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Question (5)

QN0038693

A uniform square plate has a small piece of an irregular shape removed and glued to the centre of the plate leaving a hole behind in figure. The moment of inertia about the -axis is then,

(A)
increased
(B)
decreased
(C)
the same
(D)
changed in unpredicted manner

Correct Answer: B

Explanation:

According to the question, when the small piece removed it is stick at through axis of rotation passes, but axis of rotation does not passes through and It is glued to the centre of the plate, the mass comes closer to the axis, hence, moment of inertia decreases.

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Question (6)

QN0038694

In problem-5, the of the plate is now in the following quadrant of - plane.

(A)
i
(B)
ii
(C)
iii
(D)
iv

Correct Answer: C

Explanation:

(c) Let us consider the diagram of problem 5 , there is a line shown in the figure drawn along the diagonal. First, centre of mass of the system was on the dotted line and was shifted towards from the centre (1st quadrant).

When the mass is decrease, it will be on the same line but shifted towards other side of on the line-joining or away from the centre so, new will lies in IIIrd quadrant in plane.

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Question (7)

QN0038695

The density of a non-uniform rod of length is given by where, and are constants and . The centre of mass of the rod will be at

(A)
(B)
(C)
(D)

Correct Answer: A

Explanation:

As given that density :

where and are constants and

At constant

In that case, centre of mass will be at (i.e., mid-point of the rod)

Putting, in options.
(a)
(b)
(c)
(d)

So, only (a) option gives 0.5 .

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Question (8)

QN0038696

A merry-go-round, made of a ring-like platform of radius and mass , is revolving with angular speed . A person of mass is standing on it. At one instant, the person jumps off the round, radially away from the centre of the round (as seen from the round). The speed of the round of afterwards is

(A)
(B)
(C)
(D)
0

Correct Answer: A

Explanation:

As there is external torque acting on the system, angular momentum should be conserved.

Hence constant

where, is moment of inertia of the system and is angular velocity of the system.

From Eq. (i),

where and are angular velocities before and after jumping.

So, given that,

?

as mass reduced to half, hence, moment of inertia also reduced to half:

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Question (1)

For which of the following does the centre of mass lie outside the body?

Explanation:

Link:

Question (2)

Which of the following points is the likely position of the centre of mass of the system shown in figure?

Explanation:

Link:

Question (3)

A particle of mass is moving in -plane with a uniform velocity with its trajectory running parallel to tve -axis and intersecting -axis at in figure. The change in its angular momentum about the origin as it bounces elastically from a wall at constant is

Explanation:

Link:

Question (4)

When a disc rotates with uniform angular velocity, which of following is not true?

Explanation:

Link:

Question (5)

A uniform square plate has a small piece of an irregular shape removed and glued to the centre of the plate leaving a hole behind in figure. The moment of inertia about the -axis is then,

Explanation:

Link:

Question (6)

In problem-5, the of the plate is now in the following quadrant of - plane.

Explanation:

Link:

Question (7)

The density of a non-uniform rod of length is given by where, and are constants and . The centre of mass of the rod will be at

Explanation:

Link:

Question (8)

A merry-go-round, made of a ring-like platform of radius and mass , is revolving with angular speed . A person of mass is standing on it. At one instant, the person jumps off the round, radially away from the centre of the round (as seen from the round). The speed of the round of afterwards is

Explanation:

Link:

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