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Q. No.A ball is thrown upward with an initial velocity \(v_0\) from the surface of the earth. The motion of the ball is affected by a drag force equal to \(myv^2\) (where \(m\) is mass of the ball, \(v\) is its instantaneous velocity and \(y\) is a constant). The time taken by the ball to rise to its zenith (maximum height) is:
1. \( \frac{1}{\sqrt{y g}} \tan ^{-1}\left(\sqrt{\frac{y}{g} v_0}\right) \)
2. \( \frac{1}{\sqrt{2 y g}} \tan ^{-1}\left(\sqrt{\frac{2 y}{g} v_0}\right) \)
3. \( \frac{1}{\sqrt{y g}} \sin ^{-1}\left(\sqrt{\frac{y}{g}} v_0\right) \)
4. \( \frac{1}{\sqrt{y g}}\ln\left(1+\sqrt{\frac{y}{g} v_0}\right)\)
Subtopic: Non Uniform Acceleration |
Level 4: Below 35%
JEE
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A block of mass \(2~\text{kg},\) moving with a speed of \(4~\text{m/s}\) on a horizontal surface enters a rough region extending from \(x =0.5~\text{m}\) to\(x =1.5~\text{m}.\) In this region, the retarding force is given by \(F = -kx\) with \(k=12~\text{N/m}.\) What will be the speed of the block as it just emerges from the rough surface?
1. \(0\)
2. \(1.5~\text{m/s}\)
3. \(2.0~\text{m/s}\)
4. \(2.5~\text{m/s}\)
1. \(0\)
2. \(1.5~\text{m/s}\)
3. \(2.0~\text{m/s}\)
4. \(2.5~\text{m/s}\)
Subtopic: Non Uniform Acceleration |
67%
Level 2: 60%+
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Two cars are travelling towards each other at speed of \(20\) ms-1 each. When the cars are 300 m apart, both the drivers apply brakes and the cars retard at the rate of \(2\) ms-2. The distance between them when they come to rest is :
1. \(200\) m
2. \(50\) m
3. \(100\) m
4. \(25\) m
1. \(200\) m
2. \(50\) m
3. \(100\) m
4. \(25\) m
Subtopic: Non Uniform Acceleration |
80%
Level 1: 80%+
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Q. No.
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