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Q. No.The position vector of a particle is expressed as: \(\overrightarrow{r}\left({t}\right){=}({8}{t}\hat{i}{+}{5}{t}^{2}\hat{j}{+}{6}\hat{k}).\) Which of the following statements correctly describes the direction of the particle’s acceleration?
1.
It is directed along the positive \({y \text-}\)axis.
2.
It is directed along the positive \({x \text-}\)axis.
3.
It is equally inclined to the \(x\) and \({y \text-}\)axis.
4.
It is directed along the positive \({z \text-}\)axis.
Subtopic: Acceleration |
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A projectile is launched on a horizontal surface, following a trajectory described by the equation: \(y=x-\dfrac{x^2}{20},\) where the \(y\text-\)axis is directed vertically upward. The maximum height attained by the projectile is:
(all quantities are expressed in SI units)
1. 10 m
2. 5 m
3. 20 m
4. 40 m
(all quantities are expressed in SI units)
1. 10 m
2. 5 m
3. 20 m
4. 40 m
Subtopic: Projectile Motion |
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If a projectile is launched at an angle of \(15^\circ\) with the horizontal and achieves a range of \(50~\text{m},\) what will be the range when it is launched at an angle of \(45^\circ\) with the horizontal?
| 1. | \(50~\text{m}\) | 2. | \(100~\text{m}\) |
| 3. | \(80~\text{m}\) | 4. | \(120~\text{m}\) |
Subtopic: Projectile Motion |
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Level 1: 80%+
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Given below are two statements:
| Assertion (A): | The range of a horizontal projectile is maximum when the angle of projection is \(\mathit{\theta}=45^\circ.\) |
| Reason (R): | The range is maximum when \(\mathrm{sin (2\theta})=1.\) |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | Both (A) and (R) are False. |
Subtopic: Projectile Motion |
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Level 1: 80%+
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A particle is projected at an angle of \(30^\circ\) with the ground at a speed of \(40\) m/s. The speed of the particle after two seconds is: (use \(g=10\) m/s2)
1. \(20\sqrt{2}\ \) m/s
2. \(20\sqrt{3}\ \) m/s
3. \(20\) m/s
4. \(10\sqrt{3}\) m/s
1. \(20\sqrt{2}\ \) m/s
2. \(20\sqrt{3}\ \) m/s
3. \(20\) m/s
4. \(10\sqrt{3}\) m/s
Subtopic: Projectile Motion |
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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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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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Two particles \(A\) and \(B\) are projected with speeds \(40\text{ m/s}\) and \(60\text{ m/s}\) at angles \(30^{\circ}\) and \(60^{\circ}\) above the horizontal, respectively. What is the ratio of the range of \(A\) to the range of \(B\text{?}\)
1. \(\sqrt 2 : 3\)
2. \(\sqrt 3: 2\)
3. \(4:9\)
4. \(2:1\)
1. \(\sqrt 2 : 3\)
2. \(\sqrt 3: 2\)
3. \(4:9\)
4. \(2:1\)
Subtopic: Projectile Motion |
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A particle moving in a uniform circular motion of radius \(1\) m has velocity \(3 \hat j ~\text {m/s}\) at point \(B.\) What are the velocity \((\vec{v})\)and acceleration \((\vec{a})\) at diametrically opposite point \(A?\)
| 1. | \( \vec{v}_A=3 \hat{j}~\text{m/s} ;~\vec{a}_A=-9 \hat{i}~\text{m/s}^2\) |
| 2. | \( \vec{v}_A=-3 \hat{j}~\text{m/s};~\vec{a}_A=9 \hat{i}~\text{m/s}^2\) |
| 3. | \(\vec{v}_A=-3 \hat{i}~~\text{m/s};\vec{a}_A=9 \hat{j}~\text{m/s}^2\) |
| 4. | \(\vec{v}_A=3 \hat{i}~\text{m/s} ;~\vec{a}_A=9 \hat{j}~\text{m/s}^2 \) |
Subtopic: Circular Motion |
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If a ball is thrown from the ground in a vertical plane and reaches a maximum height of \(360~\text{m},\) the maximum horizontal distance it can cover on level ground using the same launch speed is:
| 1. | \(360~\text{m}\) | 2. | \(720~\text{m}\) |
| 3. | \(1440~\text{m}\) | 4. | \(180~\text{m}\) |
Subtopic: Projectile Motion |
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