Q. No.The speed of a projectile at its maximum height is half of its initial speed. The angle of projection is:
1. \(15^{\circ}\)
2. \(30^{\circ}\)
3. \(45^{\circ}\)
4. \(60^{\circ}\)
1. \(15^{\circ}\)
2. \(30^{\circ}\)
3. \(45^{\circ}\)
4. \(60^{\circ}\)
A particle moves in the \((x\text-y)\) plane according to the rule \(x = a \sin (\omega t)\) and \(y = a \cos (\omega t)\). The particle follows:
| 1. | a circular path. |
| 2. | a parabolic path. |
| 3. | a straight line path inclined equally to x and y-axes. |
| 4. | an elliptical path. |
If two projectiles, with the same masses and with the same velocities, are thrown at an angle \(60^\circ\) and \(30^\circ\) with the horizontal, then which of the following quantities will remain the same?
| 1. | time of flight |
| 2. | horizontal range of projectile |
| 3. | maximum height acquired |
| 4. | all of the above |
A stone tied to the end of a \(1\) m long string is whirled in a horizontal circle at a constant speed. If the stone makes \(22\) revolutions in \(44\) seconds, what is the magnitude and direction of acceleration of the stone?
| 1. | \(\pi^2 ~\text{ms}^{-2} \) and direction along the tangent to the circle. |
| 2. | \(\pi^2 ~\text{ms}^{-2} \) and direction along the radius towards the centre. |
| 3. | \(\frac{\pi^2}{4}~\text{ms}^{-2} \) and direction along the radius towards the centre. |
| 4. | \(\pi^2~\text{ms}^{-2} \) and direction along the radius away from the centre. |
Two particles are projected with the same initial velocity, one makes an angle \(\theta\) with the horizontal while the other makes an angle \(\theta\) with the vertical. If their common range is \(R\), then the product of their time of flight is directly proportional to:
1. \(R\)
2. \(R^2\)
3. \(\frac{1}{R}\)
4. \(R^{0}\)
A particle \((A)\) is dropped from a height and another particle \((B)\) is projected in a horizontal direction with a speed of \(5\) m/s from the same height. The correct statement, from the following, is:
| 1. | Particle \((A)\) will reach the ground first with respect to particle \((B)\). |
| 2. | Particle \((B)\) will reach the ground first with respect to particle \((A)\). |
| 3. | Both particles will reach the ground at the same time. |
| 4. | Both particles will reach the ground at the same speed. |
A particle moves along a circle of radius \(\frac{20}{\pi}~\text{m}\) with constant tangential acceleration. If the velocity of the particle is \(80\) m/s at the end of the second revolution after motion has begun, the tangential acceleration is:
1. \(40\) ms–2
2. \(640\pi\) ms–2
3. \(160\pi\) ms–2
4. \(40\pi\) ms–2
1. \(4~\text{m/s},\) \(53^\circ\) with \(x\)-axis
2. \(4~\text{m/s},\) \(37^\circ\) with \(x\)-axis
3. \(5~\text{m/s},\) \(53^\circ\) with \(y\)-axis
4. \(5~\text{m/s},\) \(53^\circ\) with \(x\)-axis
A particle starts from the origin at \(t=0\) with a velocity of \(5.0\hat i~\text{m/s}\) and moves in the \({x\text -y}\) plane under the action of a force that produces a constant acceleration of \((3.0\hat i + 2.0 \hat j)~\text{m/s}^2.\) What is the \({y\text -}\)coordinate of the particle at the instant its \({x\text -}\)coordinate is \(84~\text m?\)
1. \(36~\text m\)
2. \(26~\text m\)
3. \(1~\text m\)
4. Zero
A particle starts from the origin at \(t=0\) with a velocity of \(5.0\hat i~\text{m/s}\) and moves in the \(x\text-y\) plane under the action of a force that produces a constant acceleration of \((3.0\hat i + 2.0\hat j)~\text{m/s}^2.\) What is the speed of the particle at the instant its \(x\text-\)coordinate is \(84~\text m?\)
1. \(36~\text{m/s}\)
2. \(26~\text{m/s}\)
3. \(1~\text{m/s}\)
4. Zero
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