Q. No.A projectile is fired so as to give a maximum horizontal range of \(1\) km. What would be the maximum height reached by it if it were to be fired vertically upward?
1.
\(2\) km
2.
\(1\) km
3.
\(\dfrac12\) km
4.
\(\dfrac14\) km
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. | \(\dfrac{h_A}{\text{sin}^2\theta}=h_B\) |
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. | \(\dfrac{1}{12}\) |
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 |
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 |
For a particle performing uniform circular motion,
| (a) | the magnitude of particle velocity (speed) remains constant. |
| (b) | particle velocity is always perpendicular to the radius vector. |
| (c) | the direction of acceleration keeps changing as the particle moves. |
| (d) | angular momentum is constant in magnitude but direction keeps changing. |
Choose the correct statement/s:
| 1. | (c), (d) | 2. | (a), (c) |
| 3. | (b), (c) | 4. | (a), (b), (c) |
In a two-dimensional motion, instantaneous speed \(v_0\) is a positive constant. Then which of the following is necessarily true?
| 1. | The average velocity is not zero at any time. |
| 2. | The average acceleration must always vanish. |
| 3. | The displacements in equal time intervals are equal. |
| 4. | Equal path lengths are traversed in equal intervals. |
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