Q. No.\({A}\) throws a ball towards \({B},\) who then catches it across the field. \({B}\) throws the ball back towards \({A},\) who then catches it. The angle of the throw is \(30^\circ\) for \({A},\) while it is \(60^\circ\) for \({B}'\text{s}\) throw. The ratio of their speeds of throw, \({v_A}: {v_B}\) is:
1. \(3\)
2. \(\dfrac13\)
3. \(\sqrt3\)
4. \(1\)
1. \(3\)
2. \(\dfrac13\)
3. \(\sqrt3\)
4. \(1\)
A man drifting on a raft on a river observes a boat moving in the same direction at a relative speed which is \(3\) times the speed of the river's flow of \(3\) km/h. The boat overtakes him at a certain moment and reaches a point downstream after a time \(T_B\) while he reaches the same point after \(T_A=3 \) hr. Then, \(T_B= \)
| 1. | \(1\) hr | 2. | \(\dfrac12\)hr |
| 3. | \(\dfrac23\) hr | 4. | \(\dfrac34\) hr |
A projectile launched at an angle \(\theta\) is observed to move at an angle of \(45^\circ\) with the vertical (upward) at some point on its trajectory. If the launch angle \(\theta\) was increased, then the horizontal range:
| 1. | decreases |
| 2. | increases |
| 3. | first increases then decreases |
| 4. | first decreases then increases |
Two guns, mounted along the forward and rear directions of a moving railroad car, are firing at the same angle (relative to the car). The shells rise to a height of 500 m. The forward range of the shells is more than the backward gun's range by 200m. The speed of the railroad car is (take g = 10 m/s2)
Hint: The range is increased/decreased due to the movement of the car by Vcar·Tshell.
1. 5 m/s
2. 10 m/s
3. 20 m/s
4. 40 m/s
A particle moves in a circle of radius \(R\) with a constant speed \(v.\) The average acceleration of the particle in during \(\left(\dfrac16\right)^{\mathrm{th}}\) revolution is:
1. \(\dfrac{v^2}{R}\)
2. \(\dfrac{2\pi v^2}{6R}\)
3. \(\dfrac{\pi v^2}{6 R}\)
4. \(\dfrac{3v^2}{\pi R}\)
The average velocity component in the horizontal direction, for a projectile projected with an initial speed u, at an angle of \(\theta\) with the horizontal is v, when the average is calculated between the point of projection and the topmost point of the trajectory.
Then, the maximum height reached (H) is related to these quantities by
1. \(u^2=\frac{v^2}{2}+gH\)
2. \(u^2=\frac{v^2}{2}-gH\)
3. \(u^2=v^2+2gH\)
4. \(u^2=v^2-2gH\)
| Assertion (A): | If two particles move with uniform accelerations in different directions, then their relative velocity changes in direction. |
| Reason (R): | Since the acceleration are in different directions, there is a relative acceleration and hence the relative velocity changes. |
| 1. | (A) is True but (R) is False. |
| 2. | (A) is False but (R) is True. |
| 3. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 4. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 1. | \(a<\dfrac{2 g}{5}\) |
| 2. | \(\dfrac{2 g}{5}< a< \dfrac{3 g}{5}\) |
| 3. | \(\dfrac {3g} {5} <a<g\) |
| 4. | \(a = g \) |
| 1. | \(v_A~\text{cos}A=v_B~\text{cos}B\) |
| 2. | \(v_A~\text{sin}A=v_B~\text{sin}B\) |
| 3. | \(\dfrac{v_A}{\text{sin}A}=\dfrac{v_B}{\text{sin}B}\) |
| 4. | \(v_A~\text{tan}A=v_B~\text{tan}B\) |
| 1. | \(ut\) | 2. | \(2ut\) |
| 3. | \(ut+\dfrac{1}{2}gt^2\) | 4. | \(2ut+gt^2\) |
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