Q. No.A ship \(A\) is moving westward with a speed of \(10~\text{kmph}\) and a ship \(B,\) \(100 ~\text{km}\) south of \(A,\) is moving northward with a speed of \(10~\text{kmph}.\) The time after which the distance between them becomes the shortest is:
1. \(0~\text{h}\)
2. \(5~\text{h}\)
3. \(5\sqrt{2}~\text{h}\)
4. \(10\sqrt{2}~\text{h}\)
1. \(0~\text{h}\)
2. \(5~\text{h}\)
3. \(5\sqrt{2}~\text{h}\)
4. \(10\sqrt{2}~\text{h}\)
\(\vec{{R}}=4 \sin (2 \pi {t}) \hat{i}+4 \cos (2 \pi {t}) \hat{j},\)
where \(R\) is in metres, \(t\) is in seconds and \({\hat{i},\hat{j}}\) denotes unit vectors along \({x}\) and \({y}\text-\)directions, respectively. Which one of the following statements is wrong for the motion of the particle?
| 1. | Acceleration is along \((\text{-}\vec R )\). |
| 2. | Magnitude of the acceleration vector is \(\frac{v^2}{R}\), where \(v\) is the velocity of the particle. |
| 3. | Magnitude of the velocity of the particle is \(8\) m/s. |
| 4. | Path of the particle is a circle of radius \(4\) m. |
A projectile is fired from the surface of the earth with a velocity of \(5~\text{m/s}\) and at an angle \(\theta\) with the horizontal. Another projectile fired from another planet with a velocity of \(3~\text{m/s}\) at the same angle follows a trajectory that is identical to the trajectory of the projectile fired from the Earth. The value of the acceleration due to gravity on the other planet is: (given \(g=9.8~\text{m/s}^2\) )
1. \(3.5~\text{m/s}^2\)
2. \(5.9~\text{m/s}^2\)
3. \(16.3~\text{m/s}^2\)
4. \(110.8~\text{m/s}^2\)
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. | \(-2\hat i-3\hat j~\) |
1. \(\theta = \tan^{-1}\left(\frac{1}{4}\right)\)
2. \(\theta = \tan^{-1}(4)\)
3. \(\theta = \tan^{-1}(2)\)
4. \(\theta = 45^{\circ}\)
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 |
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 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. \(2:1\)
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