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 |
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 |
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 |
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. | \(\dfrac{1}{12}\) |
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. | average acceleration must always vanish. |
3. | displacements in equal time intervals are equal. |
4. | equal path lengths are traversed in equal intervals. |
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 |