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Test-3 (Motion in a plane)
Q. No.

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
Subtopic:  Circular Motion |
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A projectile is fired so as to give a maximum horizontal range of \(1\) km. What would be the maximum height reached by it if it were to be fired vertically upward?
1. \(2\) km 2. \(1\) km
3. \(\dfrac12\) km 4. \(\dfrac14\) km
Subtopic:  Projectile Motion |
 55%
From NCERT

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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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A boat, when rowed perpendicular to the flow of a \(500\) m wide river, reaches its opposite bank in \(10\) min. If the boat is rowed downstream at an angle of \(30^\circ\) with the flow, it will cross in:
1. \(10\) min 2. \(5\sqrt3\) min
3. \(20\) min 4. \(\dfrac{10}{\sqrt3}\) min
Subtopic:  Relative Motion |
 60%
From NCERT

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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
Subtopic:  Projectile Motion |
 51%
From NCERT

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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 |
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Select the correct option based on the statements given below:
Statement I: When a projectile is at its highest point, its tangential acceleration is zero.
Statement II: When a projectile is at the highest point of its trajectory, its speed is minimum.
 
1. Statement I is incorrect and Statement II is correct.
2. Both Statement I and Statement II are correct.
3. Both Statement I and Statement II are incorrect.
4. Statement I is correct and Statement II is incorrect.
Subtopic:  Projectile Motion |
 64%
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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 |
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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. \(v<u\)
Subtopic:  Projectile Motion |
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Test-3 (Motion in a plane)
Q. No.

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