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 \(r\)
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:
1. | vertical |
2. | horizontal and skew with the axis |
3. | horizontal and intersecting the axis |
4. | none of these |
A body is rotating nonuniformly about a vertical axis fixed in an inertial frame. The resultant force on a particle of the body not on the axis is
1. vertical
2. horizontal and skew with the axis
3. horizontal and intersecting the axis
4. none of these
Let \(\vec{F}\) be a force acting on a particle having position vector \(\vec{r}\). Let \(\vec{\tau}\) be the torque of this force about the origin, then:
1. | \(\vec{r} \cdot \vec{\tau}=0\) and \(\vec{F} \cdot \vec{\tau}=0\) |
2. | \(\vec{r} \cdot \vec{\tau}=0\) but \(\vec{F} \cdot \vec{\tau} \neq 0\) |
3. | \(\vec{r} \cdot \vec{\tau} \neq 0\) but \(\vec{F} \cdot \vec{\tau}=0\) |
4. | \(\vec{r} \cdot \vec{\tau} \neq 0\) and \(\vec{F} \cdot \vec{\tau} \neq 0\) |