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. |
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) |
Three girls skating on a circular ice ground of radius \(200\) m start from a point \(P\) on the edge of the ground and reach a point \(Q\) diametrically opposite to \(P\) following different paths as shown in the figure. The correct relationship among the magnitude of the displacement vector for three girls will be:
1. \(A > B > C\)
2. \(C > A > B\)
3. \(B > A > C\)
4. \(A = B = C\)
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 |
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. \(\sqrt{\frac{R}{r}}\)
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 |
A cat is situated at point \(A\) (\(0,3,4\)) and a rat is situated at point \(B\) (\(5,3,-8\)). The cat is free to move but the rat is always at rest. The minimum distance travelled by the cat to catch the rat is:
1. \(5\) unit
2. \(12\) unit
3. \(13\) unit
4. \(17\) unit
The position of a moving particle at time \(t\) is \(\overrightarrow{r}=3\hat{i}+4t^{2}\hat{j}-t^{3}\hat{k}.\) Its displacement during the time interval \(t=1\) s to \(t=3\) s will be:
1. | \(\hat{j}-\hat{k}\) | 2. | \(3\hat{i}-4\hat{j}-\hat{k}\) |
3. | \(9\hat{i}+36\hat{j}-27\hat{k}\) | 4. | \(32\hat{j}-26\hat{k}\) |
Which of the following statements is incorrect?
1. | The average speed of a particle in a given time interval cannot be less than the magnitude of the average velocity. |
2. | It is possible to have a situation \(\left|\frac{d\overrightarrow {v}}{dt}\right|\neq0\) but \(\frac{d\left|\overrightarrow{v}\right|}{dt}=0\) |
3. | The average velocity of a particle is zero in a time interval. It is possible that instantaneous velocity is never zero in that interval. |
4. | It is possible to have a situation in which \(\left|\frac{d\overrightarrow{v}}{dt}\right|=0\) but \(\frac{d\left|\overrightarrow{v}\right|}{dt}\neq0\) |