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Q. No.A person can throw a ball up to a maximum range of \(100\) m. How high above the ground can he throw the same ball?
1. \(25\) m
2. \(50\) m
3. \(100\) m
4. \(200\) m
Subtopic: Projectile Motion |
From NCERT
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An object is projected in the air with initial velocity \(u\) at an angle \(\theta\). The projectile motion is such that the horizontal range \(R\), is maximum. Another object is projected in the air with a horizontal range half of the range of the first object. The initial velocity remains the same in both cases. The value of the angle of projection, at which the second object is projected, will be:
| 1. | \(45^{\circ}\) | 2. | \(30^{\circ}\) |
| 3. | \(60^{\circ}\) | 4. | \(15^{\circ}\) |
Subtopic: Projectile Motion |
70%
From NCERT
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A projectile is projected with a velocity of \(25~\text{m/s}\) at an angle \(\theta\) with the horizontal. After \(t\) seconds, its inclination with horizontal becomes zero. If \(R\) represents the horizontal range of the projectile, the value of \(\theta\) will be: (use \(g=10~\text{m/s}^2\))
1. \(\dfrac{1}{2} \sin ^{-1}\left(\dfrac{5 t^2}{4 R}\right) \)
2. \(\dfrac{1}{2} \sin ^{-1}\left(\dfrac{4 R}{5 t^2}\right) \)
3. \(\tan ^{-1}\left(\dfrac{4 \mathrm{t}^2}{5 \mathrm{R}}\right) \)
4. \(\cot ^{-1}\left(\dfrac{\mathrm{R}}{20 \mathrm{t}^2}\right)\)
1. \(\dfrac{1}{2} \sin ^{-1}\left(\dfrac{5 t^2}{4 R}\right) \)
2. \(\dfrac{1}{2} \sin ^{-1}\left(\dfrac{4 R}{5 t^2}\right) \)
3. \(\tan ^{-1}\left(\dfrac{4 \mathrm{t}^2}{5 \mathrm{R}}\right) \)
4. \(\cot ^{-1}\left(\dfrac{\mathrm{R}}{20 \mathrm{t}^2}\right)\)
Subtopic: Projectile Motion |
From NCERT
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Given below are two statements:
| Assertion (A): | Two identical balls A and B thrown with the same velocity ‘u’ at two different angles with horizontal attained the same range R. If A and B reached the maximum height h1 and h2 respectively, then \(\mathrm{R}=4 \sqrt{\mathrm{h}_1 \mathrm{~h}_2}\) |
| Reason (R): | Product of said heights, \(\mathrm{h}_1 \mathrm{~h}_2=\left(\frac{\mathrm{u}^2 \sin ^2 \theta}{2 \mathrm{~g}}\right) \cdot\left(\frac{\mathrm{u}^2 \cos ^2 \theta}{2 \mathrm{~g}}\right)\) |
| 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. | (A) is false but (R) is true. |
Subtopic: Projectile Motion |
74%
From NCERT
JEE
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For a particle in a uniform circular motion, the acceleration \(\vec a\) at any point P(R, \(\theta\)) on the circular path of radius R is: (when \(\theta\) is measured from the positive x-axis and v is uniform speed):
1. \(-\frac{v^2}{R} \sin \theta \hat{i}+\frac{v^2}{R} \cos \theta \hat{j} \)
2. \(-\frac{v^2}{R} \cos \theta \hat{i}+\frac{v^2}{R} \sin \theta \hat{j} \)
3. \(-\frac{v^2}{R} \cos \theta \hat{i}-\frac{v^2}{R} \sin \theta \hat{j} \)
4. \(-\frac{v^2}{R} \hat{i}+\frac{v^2}{R} \hat{j}\)
1. \(-\frac{v^2}{R} \sin \theta \hat{i}+\frac{v^2}{R} \cos \theta \hat{j} \)
2. \(-\frac{v^2}{R} \cos \theta \hat{i}+\frac{v^2}{R} \sin \theta \hat{j} \)
3. \(-\frac{v^2}{R} \cos \theta \hat{i}-\frac{v^2}{R} \sin \theta \hat{j} \)
4. \(-\frac{v^2}{R} \hat{i}+\frac{v^2}{R} \hat{j}\)
Subtopic: Circular Motion |
54%
From NCERT
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A projectile is launched at an angle \('\alpha'\) with the horizontal with a velocity of 20 ms-1. After 10 s, its inclination with horizontal is \(' \beta'\). The value of \(tan \beta\) will be: (g = 10 ms-2)
1. \(\tan \alpha+5 \sec \alpha \)
2. \( \tan \alpha-5 \sec \alpha \)
3. \( 2 \tan \alpha-5 \sec \alpha \)
4. \(2 \tan \alpha+5 \sec \alpha\)
1. \(\tan \alpha+5 \sec \alpha \)
2. \( \tan \alpha-5 \sec \alpha \)
3. \( 2 \tan \alpha-5 \sec \alpha \)
4. \(2 \tan \alpha+5 \sec \alpha\)
Subtopic: Projectile Motion |
76%
From NCERT
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A girl standing on the road holds her umbrella at \(45^{\circ}\) with the vertical to keep the rain away. If she starts running without an umbrella with a speed of \(15 \sqrt{2}~\text{km/h}, \) the raindrops hit her head vertically. The speed of raindrops with respect to the moving girl is:
1. \(30~\text{km/h} \)
2. \(\dfrac{25}{\sqrt{2}}~\text{km/h}\)
3. \(\dfrac{30}{\sqrt{2}}~\text{km/h}\)
4. \(25~\text{km/h} \)
1. \(30~\text{km/h} \)
2. \(\dfrac{25}{\sqrt{2}}~\text{km/h}\)
3. \(\dfrac{30}{\sqrt{2}}~\text{km/h}\)
4. \(25~\text{km/h} \)
Subtopic: Relative Motion |
From NCERT
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The motion of a particle in the \(xy \text-\)plane is described by the following equations:
\(x=4 \sin \left(\dfrac{\pi}{2}-\omega t\right)~ \text m,\) \(y=4 \sin \left(\omega t\right) ~\text m.\)
Which of the following best describes the path traced by the particle?
\(x=4 \sin \left(\dfrac{\pi}{2}-\omega t\right)~ \text m,\) \(y=4 \sin \left(\omega t\right) ~\text m.\)
Which of the following best describes the path traced by the particle?
| 1. | circular | 2. | helical |
| 3. | parabolic | 4. | elliptical |
Subtopic: Circular Motion |
63%
From NCERT
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Two inclined planes are placed as shown in the figure. A block is projected from the point \(A\) of the inclined plane \(AB\) along its surface with a velocity just sufficient to carry it to the top point \(B\) at a height of \(10~\text m.\) After reaching the point \(B\) the block slides down on the inclined plane \(BC.\) The time it takes to reach the point \(C\) from the point \(A\) is \(t( \sqrt 2 + 1 )~\text{s}.\) The value of \(t\) is:
(take \(g=10~\text{m/s}^2\))
1. \(1\)
2. \(2\)
3. \(3\)
4. \(4\)
(take \(g=10~\text{m/s}^2\))
1. \(1\)
2. \(2\)
3. \(3\)
4. \(4\)
Subtopic: Uniformly Accelerated Motion |
62%
From NCERT
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A body of mass 10 kg is projected at an angle of 45° with the horizontal. The trajectory of the body is observed to pass through a point (20, 10). If T is the time of flight, then its momentum vector, at time \(t = {T \over \sqrt 2 }\) , is _________
[Take g = 10 m/s2]
1. \(100 \hat{\mathrm{i}}+(100 \sqrt{2}-200) \hat{\mathrm{j}} \)
2. \(100 \sqrt{2} \hat{i}+(100-200 \sqrt{2}) \hat{j} \)
3. \(100 \hat{\mathrm{i}}+(100-200 \sqrt{2}) \hat{\mathrm{j}} \)
4. \(100 \sqrt{2} \hat{\mathrm{i}}+(100 \sqrt{2}-200) \hat{\mathrm{j}}\)
[Take g = 10 m/s2]
1. \(100 \hat{\mathrm{i}}+(100 \sqrt{2}-200) \hat{\mathrm{j}} \)
2. \(100 \sqrt{2} \hat{i}+(100-200 \sqrt{2}) \hat{j} \)
3. \(100 \hat{\mathrm{i}}+(100-200 \sqrt{2}) \hat{\mathrm{j}} \)
4. \(100 \sqrt{2} \hat{\mathrm{i}}+(100 \sqrt{2}-200) \hat{\mathrm{j}}\)
Subtopic: Projectile Motion |
54%
From NCERT
JEE
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