Q. No.
| 1. | \(1.4\) m | 2. | \(1.0\) m |
| 3. | \(0.8\) m | 4. | \(0.6\) m |
Rain is falling vertically downward with a speed of \(35~\text{m/s}.\) The wind starts blowing after some time with a speed of \(12~\text{m/s}\) in the east to the west direction. The direction in which a boy standing at the place should hold his umbrella is:
| 1. | \(\text{tan}^{-1}\Big(\frac{12}{37}\Big)\) with respect to rain |
| 2. | \(\text{tan}^{-1}\Big(\frac{12}{37}\Big)\) with respect to wind |
| 3. | \(\text{tan}^{-1}\Big(\frac{12}{35}\Big)\) with respect to rain |
| 4. | \(\text{tan}^{-1}\Big(\frac{12}{35}\Big)\) with respect to wind |
A particle starting from the point \((1,2)\) moves in a straight line in the \(XY\)-plane. Its coordinates at a later time are \((2,3).\) The path of the particle makes what angle with the \(x\)-axis?
1. \(30^\circ\)
2. \(45^\circ\)
3. \(60^\circ\)
4. data is insufficient
| 1. | \(10\) min | 2. | \(5\sqrt3\) min |
| 3. | \(20\) min | 4. | \(\dfrac{10}{\sqrt3}\) min |
A motorboat is racing towards the north at \(25\) km/h and the water current in that region is \(10\) km/h in the direction of \(60^\circ\) east of the south. The resultant velocity of the boat is:
| 1. | \(12\) km/h at \(23 . 4^\circ\) east of west |
| 2. | \(22\) km/h at \(23 . 4^\circ\) north of east |
| 3. | \(22\) km/h at \(23 . 4^\circ\) east of north |
| 4. | \(20\) km/h at \(23 . 4^\circ\) north of west |
1. \(4\sqrt2~\text{ms}^{-1},45^\circ\)
2. \(4\sqrt2~\text{ms}^{-1},60^\circ\)
3. \(3\sqrt2~\text{ms}^{-1},30^\circ\)
4. \(3\sqrt2~\text{ms}^{-1},45^\circ\)
The position of a particle is given by; \(\vec{{r}}=[(3.0 {t} )\hat{{i}}-(2.0 {t}^2) \hat{{j}}+(4.0) \hat{{k}} ]~\text{m},\) where \(t\) is in seconds and the coefficients have the proper units for \(\vec r\) to be in meters. What is the magnitude and direction of the velocity of the particle at \(t=2.0~\text s?\)
1. \(7.56~ \text{m} \text{s}^{-1},-70^{\circ}\text{ with} ~{y} \text{-axis}. \)
2. \(7.56~ \text{m} \text{s}^{-1}, ~70^{\circ}\text{ with} ~{x} \text{-axis}. \)
3. \(8.54 ~\text{m} \text{s}^{-1},~70^{\circ}\text{ with} ~{y} \text{-axis}. \)
4. \(8.54 ~\text{m} \text{s}^{-1},-70^{\circ}\text{ with} ~{x} \text{-axis}. \)
In a two-dimensional motion, the instantaneous speed of a particle remains constant at a positive value \(v_0.\) Which of the following statements must always be true?
| 1. | The particle has zero acceleration. |
| 2. | The particle’s acceleration is increasing. |
| 3. | The particle’s acceleration always lies in the plane of motion. |
| 4. | The particle necessarily moves in a uniform circular path. |
The following are four different relations about displacement, velocity and acceleration for the motion of a particle in general.
| (a) | \(v_{a v}=1 / 2\left[v\left(t_1\right)+v\left(t_2\right)\right]\) |
| (b) | \(v_{{av}}={r}\left({t}_2\right)-{r}\left({t}_1\right) / {t}_2-{t}_1\) |
| (c) | \(r=1 / 2\left[v\left(t_2\right)-v\left(t_1\right)\right]\left({t}_2-{t}_1\right)\) |
| (d) | \({a}_{{av}}=v\left({t}_2\right)-v\left({t}_1\right) / {t}_2-{t}_1\) |
The incorrect options is/are:
| 1. | (a) and (d) only | 2. | (a) and (c) only |
| 3. | (b) and (c) only | 4. | (a) and (b) only |
In a two-dimensional motion, instantaneous speed \(v_0\) is a positive constant. Then which of the following is necessarily true?
| 1. | The average velocity is not zero at any time. |
| 2. | The average acceleration must always vanish. |
| 3. | The displacements in equal time intervals are equal. |
| 4. | Equal path lengths are traversed in equal intervals. |
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