(a) | the number of particles to the right of the origin is equal to the number of particles to the left |
(b) | the total mass of the particles to the right of the origin is same as the total mass to the left of the origin |
(c) | the number of particles on \(x\)-axis should be equal to the number of particles on \(y\)-axis |
(d) | if there is a particle on the positive \(x\)-axis, there must be at least one particle on the negative \(x\)-axis |
Choose the correct option:
1. (a), (b) and (c)
2. (a), (b) and (d)
3. All of these
4. none of these
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?
a. | the density continuously increases from left to right. |
b. | the density continuously decreases from left to right. |
c. | the density decreases from left to right upto the centre and then increases. |
d. | the density increases from left to right upto the centre and then decreases. |
Choose the correct options:
1. | (a) and (b) |
2. | (a), (b) and (c) |
3. | all of these |
4. | none of these |
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:
1. | \(v_0=0,\) \(a_0=0\) | 2. | \(v_0=0,\) \(a_0 \neq0\) |
3. | \(v_0 \neq0,\) \(a_0=0\) | 4. | \(v_0 \neq0,\) \(a_0 \neq0\) |
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:
1. | depends on the direction of the motion of the balls. |
2. | depends on the masses of the two balls. |
3. | depends on the speeds of the two balls. |
4. | is equal to \(g.\) |
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:
1. | is zero | 2. | remains constant |
3. | goes on increasing | 4. | goes on decreasing |
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 \(r\)