Q. No.Let \(\overrightarrow{\mathrm{C}}=\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}},\) then:
1.
\(|\overrightarrow{\mathrm{C}}|\) is always greater than \(|\overrightarrow{\mathrm{A}}|\)
2.
It is possible to have \(|\overrightarrow{\mathrm{C}}|<|\overrightarrow{\mathrm{A}}|\) and \(|\overrightarrow{\mathrm{C}}|<|\overrightarrow{\mathrm{B}}|\)
3.
\(|\overrightarrow{\mathrm{C}}|\) is always equal to \(|\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}|\)
4.
\(|\overrightarrow{\mathrm{C}}|\) is never equal to \(|\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}|\)
In a projectile motion the velocity,
| 1. | is always perpendicular to the acceleration |
| 2. | is never perpendicular to the acceleration |
| 3. | is perpendicular to the acceleration for one instant only |
| 4. | is perpendicular to the acceleration for two instants |
Let \({ABCDEF} \) be a regular hexagon, with the vertices taken in order. The resultant of the vectors: \(\overrightarrow{AB},~\overrightarrow{BC},~\overrightarrow{CD},~\overrightarrow{DE} \) equals, in magnitude, the vector:
| 1. | \(\overrightarrow{AB}\) | 2. | \(\overrightarrow{AD}\) |
| 3. | \(\sqrt2\overrightarrow{AB}\) | 4. | \(\sqrt3\overrightarrow{AB}\) |
Two projectiles are launched, one at twice the speed of the other; the slower one at \(30^\circ\) and the faster one at \(60^\circ.\) Their horizontal ranges are in the ratio: (slower : faster)
| 1. | \(\dfrac{1}{2}\) | 2. | \(\dfrac{1}{4}\) |
| 3. | \(\dfrac{1}{6}\) | 4. | \(\dfrac{1}{12}\) |
Consider the two situations shown in the figures. In figure (A), the particle \(P\) is given a velocity \(u\) up a smooth horizontal incline and it reaches a maximum vertical height \(h_A\). In figure (B), the same particle \(P\) is projected with a velocity \(u\) at an angle \(\theta\) (parallel to the previous incline) and reaches a maximum height \(h_B\).Then,
| 1. | \(h_A=h_B~\text{sin}\theta\) | 2. | \(h_A~\text{sin}\theta=h_B\) |
| 3. | \(h_A~\text{sin}^2\theta=h_B\) | 4. | \(\dfrac{h_A}{\text{sin}^2\theta}=h_B\) |
| 1. | \(2\) km | 2. | \(1\) km |
| 3. | \(\dfrac12\) km | 4. | \(\dfrac14\) km |
An insect trapped in a circular groove of radius \(12~\text{cm}\) moves along the groove steadily and completes \(7\) revolutions in \(100~\text{s}.\) What is the angular speed of the motion?
1. \(0.62~\text{rad/s}\)
2. \(0.06~\text{rad/s}\)
3. \(4.40~\text{rad/s}\)
4. \(0.44~\text{rad/s}\)
1. \(4~\text{m/s},\) \(53^\circ\) with \(x\)-axis
2. \(4~\text{m/s},\) \(37^\circ\) with \(x\)-axis
3. \(5~\text{m/s},\) \(53^\circ\) with \(y\)-axis
4. \(5~\text{m/s},\) \(53^\circ\) with \(x\)-axis
Two particles having mass \(M\) and \(m\) are moving in a circular path having radius \(R\) & \(r\) respectively. If their time periods are the same, then the ratio of angular velocities will be:
1. \(\dfrac{r}{R}\)
2. \(\dfrac{R}{r}\)
3. \(1\)
4. \(\sqrt{\dfrac{R}{r}}\)
If two projectiles, with the same masses and with the same velocities, are thrown at an angle \(60^\circ\) and \(30^\circ\) with the horizontal, then which of the following quantities will remain the same?
| 1. | time of flight |
| 2. | horizontal range of projectile |
| 3. | maximum height acquired |
| 4. | all of the above |
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