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Q. No.A particle \((1),\) dropped from rest from the topmost point \((A)\) of a vertical circle, reaches the bottom \((B)\) in the same time as when a second particle \((2)\) moving with constant speed moves along the circumference from \(A\) to \(B.\) The ratio of the accelerations of the particles \((a_1/a_2)\) equals:
1.
\(1\)
2.
\(\dfrac{2}{\pi} \)
3.
\(\dfrac{4}{\pi^2} \)
4.
\(\sqrt{\dfrac{2}{\pi}} \)
Subtopic: Circular Motion |
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A particle moves around a circle with a speed of \(\pi~\text{m/s},\) while another moves back-and-forth along a diameter with a speed of \(1~\text{m/s}.\) The minimum possible relative velocity between them is (in magnitude):
1. zero
2. \((\pi-1)~\text{m/s}\)
3. \(\sqrt{\pi^2+1}~\text{m/s}\)
4. \(\sqrt{\pi^2-1}~\text{m/s}\)
1. zero
2. \((\pi-1)~\text{m/s}\)
3. \(\sqrt{\pi^2+1}~\text{m/s}\)
4. \(\sqrt{\pi^2-1}~\text{m/s}\)
Subtopic: Relative Motion |
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A ball is thrown horizontally with a speed \(u\) from the top of a tall building and it impacts the ground at a horizontal distance which is equal to the height of the building. The height of the building is:
| 1. | \(\Large\frac{u^2}{4g}\) | 2. | \(\Large\frac{u^2}{2g}\) |
| 3. | \(\Large\frac{2u^2}{g}\) | 4. | \(\Large\frac{\sqrt2u^2}{g}\) |
Subtopic: Projectile Motion |
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A man walks in the rain, where the raindrops are falling vertically down at a constant speed of \(4~\text{m/s}\) relative to ground. Let the relative velocity of a droplet with respect to man be \(v_r\) and let it make an angle \(\theta_r\) with the vertical. Then:
1. \(v_r=4\cos\theta_r~\text{m/s}\)
2. \(v_r=4\sin\theta_r~\text{m/s}\)
3. \(v_r=4\sec\theta_r~\text{m/s}\)
4. \(v_r=4~\mathrm{cosec }\theta_r~\text{m/s}\)
1. \(v_r=4\cos\theta_r~\text{m/s}\)
2. \(v_r=4\sin\theta_r~\text{m/s}\)
3. \(v_r=4\sec\theta_r~\text{m/s}\)
4. \(v_r=4~\mathrm{cosec }\theta_r~\text{m/s}\)
Subtopic: Relative Motion |
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A ball is thrown at an angle \(\theta_0\) above the horizontal, and follows the parabolic path taken by a projectile. Let its speed be \(v\) when its trajectory makes an angle \(\theta\) with the horizontal. Assuming \(A\) to be a constant,
1. \(v=A\cos\theta\)
2. \(v=A\sin\theta\)
3. \(v=A\tan\theta\)
4. \(v=A\sec\theta\)
1. \(v=A\cos\theta\)
2. \(v=A\sin\theta\)
3. \(v=A\tan\theta\)
4. \(v=A\sec\theta\)
Subtopic: Projectile Motion |
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The acceleration of a projectile, in the direction of its motion:
| 1. | is always positive |
| 2. | is always negative |
| 3. | maybe positive, negative or zero |
| 4. | is always non-zero |
Subtopic: Projectile Motion |
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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 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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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 |
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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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