A body has its centre of mass at the origin. The x–coordinates of the particles:

(a) may be all positive

(b) may be all negative

(c) may be all non-negative

(d) may be positive for some case and negative in other cases

Choose the correct option:

1. (a) and (b)

2. (b) and (c)

3. (c) and (d)

4. All of these

In which of the following cases the centre of mass of a rod is certainly not at its centre?
 

Choose the correct options:

If the external forces acting on a system have zero resultant, the centre of mass:

(a) must not move

(b) must not accelerate

(c) may move

(d) may accelerate

Choose the correct options:

1. (a) and (b)

2. (b) and (c)

3. (c) and (d)

4. All of these

A nonzero external force acts on a system of particles. The velocity and the acceleration of the centre of mass are found to be \(v_0\) and \(a_0\) at an instant \(t.\) It is possible that:
(a) \(v_0=0,\) \(a_0=0\)
(b) \(v_0=0,\) \(a_0 \neq0\)
(c) \(v_0 \neq0,\) \(a_0=0\)
(d) \(v_0 \neq0,\) \(a_0 \neq0\)
Choose the correct options:
1. (a) and (b)
2. (b) and (c)
3. (c) and (d)
4. (b) and (d)

Two balls are thrown simultaneously in the air. The acceleration of the centre of mass of the two balls while in the air:

Let \(\overrightarrow A\) be a unit vector along the axis of rotation of a purely rotating body and \(\overrightarrow B\) be a unit vector along the velocity of a particle P of the body away from the axis. The value of \(\overrightarrow A.\overrightarrow B\) is:
1. \(1\)
2. \(-1\)
3. \(0\)
4. None of these

A body is uniformly rotating about an axis fixed in an inertial frame of reference. Let \(\overrightarrow A\) be a unit vector along the axis of rotation and \(\overrightarrow B\) be the unit vector along the resultant force on a particle P of the body away from the axis. The value of \(\overrightarrow A.\overrightarrow B\) is:

1. 1

2. –1

3. 0

4. none of these

A particle moves with a constant velocity parallel to the X-axis. Its angular momentum with respect to the origin:

A body is in pure rotation. The linear speed \(v\) of a particle, the distance \(r\) of the particle from the axis and the angular velocity \(\omega\) of the body are related as \(w=\dfrac{v}{r}\). Thus:
1. \(w\propto\dfrac{1}{r}\)
2. \(w\propto\ r\)
3. \(w=0\)
4. \(w\) is independent of \(r\)

A body is rotating uniformly about a vertical axis fixed in an inertial frame. The resultant force on a particle of the body not on the axis is: