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Q. No.Given below are two statements:
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).
Subtopic: Relative Motion |
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A particle is released from the top of a smooth hemisphere of radius \(R,\) and it slides down along its surface. After it slides down a height \(\frac R5,\) its acceleration will be \(a,\) where:
| 1. | \(a<\dfrac{2 g}{5}\) |
| 2. | \(\dfrac{2 g}{5}< a< \dfrac{3 g}{5}\) |
| 3. | \(\dfrac {3g} {5} <a<g\) |
| 4. | \(a = g \) |
Subtopic: Circular Motion |
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Two particles \(A\), \(B\) are projected simultaneously from the base of a triangle \(ABC\). Particle \(A\) is projected from vertex \(A\) along \(AC,\) and particle \(B\) is projected from vertex \(B\) along \(BC\). Their respective velocities are \(v_A\) & \(v_B\) and they move with uniform velocities. For the particles to collide:
| 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. | \(v_A~\text{tan}A=v_B~\text{tan}B\) |
Subtopic: Relative Motion |
51%
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Particles are simultaneously projected in all possible directions from a point in space, located in a uniform gravitational field. The initial speed of the particle is \(u.\) The maximum separation between any two particles, after a time \(t,\) is:
| 1. | \(ut\) | 2. | \(2ut\) |
| 3. | \(ut+\dfrac{1}{2}gt^2\) | 4. | \(2ut+gt^2\) |
Subtopic: Projectile Motion |
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The average velocity of a projectile from the point of projection to impact is \(v_1\) while the average velocity from projection to maximum height\((H)\) is \(v_2\).
It can be concluded that:
It can be concluded that:
| 1. | \(v_1>v_2\) |
| 2. | \(v_1<v_2\) |
| 3. | \(v_1=v_2\) |
| 4. | Any of the above can be true depending on the angle of projection |
Subtopic: Projectile Motion |
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A ball is thrown up with a speed \(u\) at an angle of \(60^{\circ}\) with the horizontal; the thrower of the ball runs with a uniform speed \(v\) and stops suddenly when he reaches a certain point. He observes that the ball is at its maximum height, and then waits until it reaches him. Then
1. \(v=4u\)
2. \(v=2u\)
3. \(v=u\)
4. \(v<u\)
1. \(v=4u\)
2. \(v=2u\)
3. \(v=u\)
4. \(v<u\)
Subtopic: Projectile Motion |
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A projectile is launched at an angle \(\theta~(<90^{\circ})\) above the horizontal. Its velocity is measured along the direction of projection and is plotted against time and the magnitudes of the slopes are indicated in the figure below. Which of the following is the correct graph?
1. \(a\)
2. \(b\)
3. \(c\)
4. \(d\)
Subtopic: Projectile Motion |
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Two particles \(A\) and \(B\) start moving uniformly along the periphery of a circle, \(A\) making \(2\) revolutions/min and \(B\) making \(3\) revolutions/min. \(A\) and \(B\) start from the same point, moving in opposite directions. After what minimum time will they meet at their starting point?
1. \(1\) min
2. \(6\) min
3. \(0.5\) min
4. \(\dfrac {1}{6}\) min
1. \(1\) min
2. \(6\) min
3. \(0.5\) min
4. \(\dfrac {1}{6}\) min
Subtopic: Circular Motion |
50%
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Two particles \(A,B\) move along the periphery of a circle of radius \(R,\) with the same uniform speed \(u.\) Particle \(A\) follows \(B,\) a quarter of the circumference behind it. The acceleration of \(A\) relative to \(B\) is:
| 1. | zero | 2. | \(\dfrac{2u^2}{R}\) |
| 3. | \(\dfrac{u^2}{\sqrt2R}\) | 4. | \(\dfrac{\sqrt2u^2}{R}\) |
Subtopic: Circular Motion |
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Two projectiles are fired simultaneously from the same point, one \((A)\)-vertically upward and the other \((B)\)-at some angle with the vertical. Both projectiles reach their maximum height above the ground simultaneously. Their separation at this instant is \(1600\) m. The range of the second projectile \((B)\) is:
1. \(2.4\) km
2. \(1.6\sqrt{3}\) km
3. \(1.6\sqrt2\) km
4. \(3.2\) km
1. \(2.4\) km
2. \(1.6\sqrt{3}\) km
3. \(1.6\sqrt2\) km
4. \(3.2\) km
Subtopic: Projectile Motion |
56%
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