Systems of Particles and Rotational Motion Test

Result

Systems of Particles and Rotational Motion Test - 79

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Question 1
4 / -1

Three masses of 2 kg, 4 kg and 4 kg are placed at the three points ( 1, 0, 0), (1, 1, 0) and (0, 1, 0) respectively. The position vector of its centre of mass is

A

B

C

D

Solution
Question 2
4 / -1

A man of 50 kg mass it standing in gravity free space at a height of 10 m above the floor. He throws a stone of 0.5 kg mass downwards with a speed of 2 m/s. When the stone reached the floor, the distance of the man above the floor will be

A
20 m

B
9.9 m

C
10.1 m

D
10 m

Solution
Question 3
4 / -1

A
10/3

B
5/2

C
1/2

D
2/5

Solution
Question 4
4 / -1

Two persons of masses 55 kg and 65 kg respectively, are at the opposite ends of a boat. The length of the boat is 3.0 m and weight 100 kg. The 55 kg man walks up to the 65 kg man and sits with him. If the boat is in still water the centre of mass of the system shifts by

A
3.0 m

B
2.3 m

C
zero

D
0.75 m

Solution
Question 5
4 / -1

In a bicycle the radius of rear wheel is twice the radius of front wheel. If r_F and r_r are the radius, v_F and v_r are speeds of top most points of wheel, then

A
v_r = 2v_F

B
v_F = 2v_r

C
v_F = v_r

D
v_F > v_r
Question 6
4 / -1

A wheel is rolling along the ground with a speed of 2 ms^–1. The magnitude of the velocity of the points at the extremities of the horizontal diameter of the wheel is equal to

A

B

C

D

Solution
Question 7
4 / -1

A point P on the rim of wheel is initially at rest and in contact with the ground. Find the displacement of the point P if the radius of the wheel is 5 m and the wheel rolls forward through half a revolution

A
5 m

B
10 m

C
2.5 m

D

Solution
Question 8
4 / -1

A wheel has angular acceleration of 3.0 rad/sec² and an initial angular speed of 2.00 rad/sec. In a time of 2 sec it has rotated through an angle (In radian) of

A
6

B
10

C
12

D
4

Solution
Question 9
4 / -1

When a ceiling fan is switched on, it makes 10 revolutions in the first 3 seconds. Assuming a uniform angular acceleration, how many rotations it will make in the next 3 seconds?

A
10

B
20

C
30

D
40

Solution
Question 10
4 / -1

The general motion of a rigid body can be considered to be a combination of (i) a motion of its centre of mass about an axis, and (ii) its motion about an instantaneous axis passing through the centre of mass.
These axes need not be stationary. Consider, for example, a thin uniform disc welded (rigidly fixed) horizontally at its rim to a massless stick, as shown in the figure.
When the disc-stick system is rotated about the origin on a horizontal frictionless plane with angular speed co, the motion at any instant can be taken as a combination of (i) a rotation of the centre of mass of the disc about the z-axis, and (ii) a rotation of the disc through an instantaneous vertical axis passing through its centre of mass (as is seen from the changed orientation of points P and Q).
Both these motions have the same angular speed ω this case.

A
It is vertical for both the cases A and B.

B
It is vertical for case A and is at 45° to the x–z plane and lies in the plane of the disc for case B.

C
It is horizontal for case A and is at 45° to the x–z plane and is normal to the plane of the disc for case B.

D
It is vertical for case A and is at 45° to the x–z plane and is normal to the plane of the disc for case B.