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Q. No.A car starts at point \(X.\) It travels \(3.0\) km due east, then \(4.0\) km due south, then \(6.0\) km due west, and finally \(8.0\) km due north. How far away is the car from point \(X\) when it has reached the end of this journey? (Assume that all distances moved are on a flat horizontal surface and that point \(X\) is on the equator. You may ignore any curvature of the Earth).
1.
\(5.0\) km
2.
\(21.0\) km
3.
\(10.0\) km
4.
\(7.0\) km
Subtopic: Position & Displacement |
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A cricket ball is thrown with a speed of \(32\text{ m/s}\) at an angle of \(30^{\circ}\) above the horizontal. The maximum height it will attain is: (take \(g=10\text{ m/s}^2\))
1. \(0.8~\text{m}\)
2. \(12.8~\text{m}\)
3. \(25.6~\text{m}\)
4. \(51.2~\text{m}\)
1. \(0.8~\text{m}\)
2. \(12.8~\text{m}\)
3. \(25.6~\text{m}\)
4. \(51.2~\text{m}\)
Subtopic: Projectile Motion |
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A ball is thrown upward at an angle of \(45^{\circ}\) with the vertical and velocity \(v\). During its entire journey, we can say:
| 1. | its total momentum will be constant. |
| 2. | its total energy will not be constant. |
| 3. | its vertical component of momentum will be constant. |
| 4. | its horizontal component of momentum will be constant. |
Subtopic: Projectile Motion |
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A body of mass \(m\) is moving in a horizontal circle of radius \(R\) with a frequency \(\nu.\) Which of the following represents the magnitude of the centripetal acceleration acting on the body?
| 1. | \(4m\pi \nu^2R \) | 2. | \(4\pi^2 \nu R \) |
| 3. | \(4\pi^2 \nu^2R \) | 4. | \(4\pi^2 \nu^2R^2 \) |
Subtopic: Circular Motion |
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A particle of a mass \(m\) is moving in a circle of the radius \(r\) with uniform speed \(v.\) Choose the correct option:
| 1. | radial acceleration \(a_{r}=0;\) tangential acceleration \(a_{t}\neq 0.\) |
| 2. | radial acceleration \(a_{r}=0;\) tangential acceleration \(a_{t}=0.\) |
| 3. | radial acceleration \(a_{r}\neq 0;\) tangential acceleration \(a_{t}\neq 0.\) |
| 4. | radial acceleration \(a_{r}\neq 0;\) tangential acceleration \(a_{t}=0\) |
Subtopic: Circular Motion |
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An insect trapped in a circular groove of radius \(10\text{ cm}\) moves along the groove steadily and completes \(14\) revolutions in \(100\text{ s.}\) The angular speed of the insect is: \(\Big(\text{Take }\pi=\dfrac{22}{7}\Big)\)
1. \(0.22\text{ rad/s}\)
2. \(0.44\text{ rad/s}\)
3. \(0.88\text{ rad/s}\)
4. \(1.76\text{ rad/s}\)
1. \(0.22\text{ rad/s}\)
2. \(0.44\text{ rad/s}\)
3. \(0.88\text{ rad/s}\)
4. \(1.76\text{ rad/s}\)
Subtopic: Circular Motion |
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A batsman hits a ball with a speed of \(14\sqrt2 \) ms–1 in a direction \(45^\circ\) above the horizontal. The maximum height attained by the ball will be:
| 1. | \(20.0\) m | 2. | \(10.0\) m |
| 3. | \(\dfrac{\sqrt2}{0.7}\) m | 4. | \(14\sqrt2\) m |
Subtopic: Projectile Motion |
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A projectile is thrown with an initial velocity \(v_0\) from the ground at an angle \(\theta\) with the horizontal direction. Which of the following statements is correct during its entire journey? (ignoring air resistance)
| 1. | Horizontal component of the linear momentum of the projectile is constant during its motion. |
| 2. | Velocity of the projectile is zero at the maximum height. |
| 3. | Acceleration of the projectile is zero at the maximum height. |
| 4. | Displacement of the projectile in a horizontal direction is zero. |
Subtopic: Projectile Motion |
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A person starts from home to reach the market. First he goes \(50\) m due north, then \(30\) m due east and finally \(50\) m due south. His displacement from home is:
| 1. | \(80\) m due south | 2. | \(80\) m due east |
| 3. | \(30\) m due south | 4. | \(30\) m due east |
Subtopic: Position & Displacement |
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Two particles are projected in the air at the same speed \(u\) at an angle \(\theta_1 \) and \(\theta_2\) (\(\theta_1 \) and \(\theta_2\) are acute angles) to the horizontal, respectively. If the maximum height reached by the first particle is greater than that of the second, then which of the following is correct?
(\(T_1\) and \(T_2\) are the times of flight of the two particles respectively)
1. \(\theta_1>\theta_2\)
2. \(\theta_1=\theta_2\)
3. \(T_1<T_2\)
4. \(T_1=T_2\)
(\(T_1\) and \(T_2\) are the times of flight of the two particles respectively)
1. \(\theta_1>\theta_2\)
2. \(\theta_1=\theta_2\)
3. \(T_1<T_2\)
4. \(T_1=T_2\)
Subtopic: Projectile Motion |
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