Q. No.A missile is fired for a maximum range with an initial velocity of \(20~\text {m/s}.\) If \(g=10~\text{m/s}^2,\) then the range of the missile will be:
1.
\(50~\text m\)
2.
\(60~\text m\)
3.
\(20~\text m\)
4.
\(40~\text m\)
A particle of mass m is projected with velocity v making an angle of 45° with the horizontal. When the particle lands on level ground, the magnitude of change in its momentum will be:
1.
2.
3.
4. zero
For a projectile projected at angles \((45^{\circ}-\theta)\) and \((45^{\circ}+\theta)\), the horizontal ranges described by the projectile are in the ratio of:
1. \(1:1\)
2. \(2:3\)
3. \(1:2\)
4. \(2:1\)
A car turns at a constant speed on a circular track of radius \(100~\text m,\) taking \(62.8~\text s\) for every circular lap. The average velocity and average speed for each circular lap, respectively, is:
| 1. | \(0,~0\) | 2. | \(0,\) \(10~\text{m/s},\) |
| 3. | \(10~\text{m/s},\) \(10~\text{m/s},\) | 4. | \(10~\text{m/s},\) \(0\) |
The speed of a swimmer in still water is \(20~\text{m/s}.\) The speed of river water is \(10~\text{m/s}\) and is flowing due east. If he is standing on the south bank and wishes to cross the river along the shortest path, the angle at which he should make his strokes with respect to the north is given by:
| 1. | \(45^{\circ}\) west of north | 2. | \(30^{\circ}\) west of north |
| 3. | \(0^{\circ}\) west of north | 4. | \(60^{\circ}\) west of north |
Two particles \(A\) and \(B\) are moving in a uniform circular motion in concentric circles of radii \(r_A\) and \(r_B\) with speeds \(v_A\) and \(v_B\) respectively. Their time periods of rotation are the same. The ratio of the angular speed of \(A\) to that of \(B\) will be:
| 1. | \( 1: 1 \) | 2. | \(r_A: r_B \) |
| 3. | \(v_A: v_B \) | 4. | \(r_B: r_A\) |
A body is moving with a velocity of \(30~\text{m/s}\) towards the east. After \(10~\text s,\) its velocity becomes \(40~\text{m/s}\) towards the north. The average acceleration of the body is:
1. \( 7~\text{m/s}^2\)
2. \( \sqrt{7}~\text{m/s}^2\)
3. \(5~\text{m/s}^2\)
4. \(1~\text{m/s}^2\)
A particle moves in a circle of radius \(5\) cm with constant speed and time period \(0.2\pi\) s. The acceleration of the particle is:
| 1. | \(25\) m/s2 | 2. | \(36\) m/s2 |
| 3. | \(5\) m/s2 | 4. | \(15\) m/s2 |
1. \(\theta = \tan^{-1}\left(\frac{1}{4}\right)\)
2. \(\theta = \tan^{-1}(4)\)
3. \(\theta = \tan^{-1}(2)\)
4. \(\theta = 45^{\circ}\)
The velocity of a projectile at the initial point \(A\) is \(2\hat i+3\hat j~\text{m/s}.\) Its velocity (in m/s) at the point \(B\) is:
| 1. | \(-2\hat i+3\hat j~\) | 2. | \(2\hat i-3\hat j~\) |
| 3. | \(2\hat i+3\hat j~\) | 4. | \(-2\hat i-3\hat j~\) |
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