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Q. No.A particle is moving with a velocity \(\vec v=K(y \hat{i}+x\hat{j}),\) where \(K\) is a constant. The general equation for its path is:
1. \(y=x^2+\text{constant}\)
2. \(y^2=x+\text{constant}\)
3. \(y^2=x^2+\text{constant}\)
4. \(xy=\text{constant}\)
Subtopic: Speed & Velocity |
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Level 2: 60%+
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The machine as shown has \(2\) rods of length \(1~\text{m}\) connected by a pivot at the top. The end of one rod is connected to the floor by a stationary pivot and the end of the other rod has a roller that rolls along the floor in a slot. As the roller goes back and forth, a \(2~\text{kg}\) weight moves up and down. If the roller is moving towards the right at a constant speed, the weight moves up with a:
| 1. | speed which is \(\frac{3}{4}\text{th}\) of that of the roller when the weight is \(0.4~\text{m}\) above the ground |
| 2. | constant speed |
| 3. | decreasing speed |
| 4. | increasing speed |
Subtopic: Speed & Velocity |
Level 4: Below 35%
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The displacement of a particle changes with time as \({x}=6 t^3-12 t^2+20 t+30.\) The velocity of the particle when its acceleration becomes zero (\(t\) is time in \(\text s\)) is:
1. \(12~\text{m/s}\)
2. \(14~\text{m/s}\)
3. \(18~\text{m/s}\)
4. \(20~\text{m/s}\)
1. \(12~\text{m/s}\)
2. \(14~\text{m/s}\)
3. \(18~\text{m/s}\)
4. \(20~\text{m/s}\)
Subtopic: Speed & Velocity |
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Level 1: 80%+
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A ball is thrown from point \(O\) at the base of a staircase. Each step has dimensions of \((0.5 ~\text{m} \times 0.5 ~\text{m})\)(width\(\times\)height). What is the minimum initial speed required for the ball to land directly on the \(5^\mathrm{th}\) step using projectile motion?
| 1. | \(5 \sqrt{(\sqrt{2}+1})~\text{m/s}\) | 2. | \(5\sqrt{2}~\text{m/s}\) |
| 3. | \(5(\sqrt{2}+1)~\text{m/s}\) | 4. | \(6 \sqrt{(\sqrt{3}+1})~\text{m/s}\) |
Subtopic: Projectile Motion |
Level 3: 35%-60%
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Two particles are moving along the same circular path. If the ratio of their centripetal accelerations is \(3:4,\) then the ratio of their tangential velocities is:
| 1. | \(2:\sqrt3\) | 2. | \(\sqrt3:2 \) |
| 3. | \(\sqrt3:1\) | 4. | \(1:\sqrt{3}\) |
Subtopic: Circular Motion |
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Level 1: 80%+
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A particle has an initial \((t = 0)\) velocity \(\vec{u}=5 \hat{i}\) and is at its origin at this instant. Its acceleration is given by \((3\hat{i}+4\hat{j}).\) When the particles \(x\) co-ordinate is \(16\) units, then its speed is:
1. \(13\) units
2. \(\sqrt{161}\) units
3. \(12\) units
4. \(\sqrt{185}\) units
1. \(13\) units
2. \(\sqrt{161}\) units
3. \(12\) units
4. \(\sqrt{185}\) units
Subtopic: Speed & Velocity |
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Level 2: 60%+
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A cyclist starts from the point P of a circular ground of radius \(2\) km and travels along its circumference to the point S. The displacement of a cyclist is –
1. \(4\) km
2. \(6\) km
3. \(\sqrt{8}\) km
4. \(8\) km
1. \(4\) km
2. \(6\) km
3. \(\sqrt{8}\) km
4. \(8\) km
Subtopic: Position & Displacement |
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A clock has \(75 \mathrm{~cm}, 60 \mathrm{~cm}\) long second hand and minute hand respectively. In \(30\) minutes duration the tip of second hand will travel \({x}\) distance more than the tip of minute hand. The value of \(\mathrm{x}\) in meter is nearly (Take \(\pi=3.14\) ) :
1. \(118.9\)
2. \(220.0\)
3. \(139.4\)
4. \(140.5\)
1. \(118.9\)
2. \(220.0\)
3. \(139.4\)
4. \(140.5\)
Subtopic: Circular Motion |
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Level 3: 35%-60%
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A particle is projected at an angle of \(30^{\circ}\) with the horizontal. It is observed that the particle reaches the same height at \(3~\text{s}\) and \(5~\text{s}\) after projection. The initial projection speed is: \(\left ( \text{take}~g=10~\text{m/s}^2 \right) \)
| 1. | \(40~\text{m/s}\) | 2. | \(50~\text{m/s}\) |
| 3. | \(80~\text{m/s}\) | 4. | \(60~\text{m/s}\) |
Subtopic: Projectile Motion |
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Level 2: 60%+
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Two projectiles, \(A\) and \(B\) are projected from the same point \((O)\) on the ground with the same initial speed, as shown in the figure. The ratio of maximum height attained by the projectile \(A\) to that attained by projectile \(B\) is:
| 1. | \(3 : 1\) | 2. | \(1 : 3\) |
| 3. | \(\sqrt 3 : 1\) | 4. | \(\sqrt 3 : 2\) |
Subtopic: Projectile Motion |
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Level 2: 60%+
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