Motion of System of Particles and Rigid Body Test

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Motion of System of Particles and Rigid Body Test - 5

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Question 1
1 / -0

Four spheres each of mass m and diameter 2r are located with their centres on four corners of a square of side a (> 2r). The moment of inertia of the system about one side of the sphere is

A

B

C

D
Question 2
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A sphere is rolling on an inclined plane. What is the ratio of its rotational KE to the total KE?

A
2 : 7

B
3 : 1

C
1 : 2

D
2 : 1
Question 3
1 / -0

A rod of mass M and length L is pivoted about its end O as shown in the figure. Find the period of SHM.

A
2

B
2

C
2

D
Question 4
1 / -0

A disc of mass 2 kg and radius 0.2 m is rotating with an angular velocity of 30 rad/s. What is the angular velocity if a mass of 0.25 kg is put on the periphery of the disc?

A
24 rad/s

B
36 rad/s

C
15 rad/s

D
26 rad/s
Question 5
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The moment of inertia of a body does not depend upon

A
the angular velocity of the body

B
the mass of the body

C
the axis of rotation of the body

D
All of the above
Question 6
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A circular disc of radius R is removed from a bigger circular disc of radius 2R as shown in the figure. The centre of mass of the new disc is αR from the centre of the bigger disc. What is the value of α?

A

B

C

D
Question 7
1 / -0

The ratio of the radius of gyration of a circular disc about a tangential axis in the plane of the disc and that of a circular ring of the same radius about a tangential axis in the plane of the ring is

A
2 : 3

B
2 : 1

C

D
1 :
Question 8
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Directions: The following question has four choices out of which ONLY ONE is correct.

Four cubes of side 'a' each of mass 40 g, 20g, 10 g and 20 g are arranged in the X – Y plane as shown in fig. The co-ordinates of the centre of mass of the combination with respect to 0 are:

A

B

C

D
Question 9
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Two spheres, each of mass 'M' and radius 'R ⁄ 2', are connected with a massless rod of length '2R' as shown in the figure. What will be the moment of inertia of the system about an axis passing through the centre of one of the spheres, perpendicular to the rod?

A

B

C

D
Question 10
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Identify the correct statement(s) about the centre of mass.

A
At the centre of mass, the entire mass of the body is concentrated.

B
The centre of mass of a body may lie inside or outside the body.

C
The centre of mass always lies on the axis of symmetry, if it exists.

D
All of the above
Question 11
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An electric motor exerts a constant torque of 10 N^-m on a grind stone mounted on a shaft. Moment of inertia of the grind stone about the shaft is 2 kg m². If the system starts from rest, find the work done in 8 s.

A
1600 J

B
1200 J

C
800 J

D
600 J
Question 12
1 / -0

The distance between the centres of carbon and oxygen atoms in carbon monoxide molecule is 1.130 x 10^-10 m. Locate the centre of mass of the molecule relative to the carbon atom.

A
_5.428

B
_1.130

C
_0.6457

D
_0.326
Question 13
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Directions: The following question contains statement-1 (Assertion) and statement-2 (Reason) followed by 4 choices (1), (2), (3) and (4), out of which ONLY ONE is correct.

Statement-1:
If there is no external torque on a body about its centre of mass, the velocity of the centre of mass remains constant.
Statement-2:
The linear momentum of an isolated system remains constant.

A
Statement-1 is True, statement-2 is True; statement-2 is the correct explanation for statement-1.

B
Statement-1 is True, statement-2 is True; statement-2 is not the correct explanation for statement-1.

C
Statement-1 is True, statement-2 is False.

D
Statement-1 is False, statement-2 is True.
Question 14
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A hollow cylinder and a solid cylinder having the same mass and the same diameter are released from rest simultaneously from the top of an inclined plane. Which will reach the bottom first?

A
Solid cylinder will reach the bottom first.

B
Hollow cylinder will reach the bottom first.

C
Both will reach the bottom together.

D
Cylinder with greater density will reach the bottom first.