Q. No.Let \(\mathrm{ABCDEF}\) 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. \(\sqrt3\overrightarrow{AB}\)
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. \(\frac{1}{2}\)
2. \(\frac{1}{4}\)
3. \(\frac{1}{6}\)
4. \(\frac{1}{12}\)
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 \(\overrightarrow{\mathrm{C}}=\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}},\) then:
| 1. | \(|\overrightarrow{\mathrm{C}}|\) is always greater than \(|\overrightarrow{\mathrm{A}}|\) |
| 2. | It is possible to have \(|\overrightarrow{\mathrm{C}}|<|\overrightarrow{\mathrm{A}}|\) |
| 3. | \(|\overrightarrow{\mathrm{C}}|\) is always equal to \(|\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}|\) |
| 4. | \(|\overrightarrow{\mathrm{C}}|\) is never equal to \(|\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}|\) |
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. | \(\frac{h_A}{\text{sin}^2\theta}=h_B\) |
1. \(2\) km
2. \(1\) km
3. \(\dfrac12\) km
4. \(\dfrac14\) km
An insect trapped in a circular groove of radius \(12\) cm moves along the groove steadily and completes \(7\) revolutions in \(100\) s. What is the angular speed of the motion?
1.\(0.62\) rad/s
2.\(0.06\) rad/s
3. \(4.40\) rad/s
4. \(0.44\) rad/s
The position of a particle is given by; \(\vec{r}=(3.0t\hat{i}-2.0t^{2}\hat{j}+4.0\hat{k})\) m
where \(t\) is in seconds and the coefficients have the proper units for \(r\) to be in meters. The magnitude and direction of \(\vec{v}(t)\) at \(t=1.0\) s are:
| 1. | \(4\) m/s \(53^\circ\) with x-axis |
| 2. | \(4\) m/s \(37^\circ\) with x-axis |
| 3. | \(5\) m/s \(53^\circ\) with y-axis |
| 4. | \(5\) 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. \(\frac{r}{R}\)
2. \(\frac{R}{r}\)
3. \(1\)
4. \(\sqrt{\frac{R}{r}}\)
If two projectiles, with the same masses and with the same velocities, are thrown at an angle \(60^\circ\) & \(30^\circ\) 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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