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Q. No.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 |
51%
Level 3: 35%-60%
Hints
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 |
61%
Level 2: 60%+
Hints
A projectile is fired from the top of a cliff, the maximum range of the projectile being \(1000\) m on level ground. The maximum range of the projectile, measured from the base of the cliff is:
| 1. | greater than \(1000\) m |
| 2. | less than \(1000\) m |
| 3. | equal to \(1000\) m |
| 4. | can be any of the above depending on the height of the cliff |
Subtopic: Projectile Motion |
Level 3: 35%-60%
Hints
A tangential force, constant in magnitude, acts on a particle moving in a circular path. This kind of force is:
| 1. | conservative |
| 2. | non-conservative |
| 3. | neither conservative nor non-conservative |
| 4. | either conservative or non-conservative depending on whether the force is acting forward or backward |
Subtopic: Circular Motion |
50%
Level 3: 35%-60%
Hints
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 |
51%
Level 3: 35%-60%
Hints
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 |
Level 3: 35%-60%
Hints
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 |
Level 3: 35%-60%
Hints
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 |
Level 3: 35%-60%
Hints
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 |
50%
Level 3: 35%-60%
Hints
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 |
54%
Level 3: 35%-60%
Hints
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