Q. No.In a two-dimensional motion, instantaneous speed 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 remains directly 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.
2.
3.
4.
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. \(\sqrt{\frac{R}{r}}\)
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 |
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 \(\vec{r}=3\hat{i}+4t^{2}\hat{j}-t^{3}\hat{k}.\) 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 \(|\frac{d\vec{v}}{dt}|\neq0\) but \(\frac{d|\vec{v}|}{dt}=0\) |
| 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 \(|\frac{d\vec{v}}{dt}|=0\) but \(\frac{d|\vec{v}|}{dt}\neq0\) |
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