A particle is moving with velocity \(\overrightarrow{v} = k \left(y \hat{i} + x \hat{j}\right)\) where \(k\) is a constant. The general equation for the path will be:
1. | \(y = x^2+ \text{constant}\) | 2. | \(y^2=x^2+ \text{constant}\) |
3. | \(y= x+ \text{constant}\) | 4. | \(xy= \text{constant}\) |
A body is thrown vertically so as to reach its maximum height in \(t\) second. The total time from the time of projection to reach a point at half of its maximum height while returning (in second) is:
1. \(\sqrt{2} t\)
2. \(\left(1 + \frac{1}{\sqrt{2}}\right) t\)
3. \(\frac{3 t}{2}\)
4. \(\frac{t}{\sqrt{2}}\)
Three particles are moving with constant velocities \(v_1 ,v_2\) and \(v\) respectively as given in the figure. After some time, if all the three particles are in the same line, then the relation among \(v_1 ,v_2\) and \(v\) is:
1. \(v =v_1+v_2\)
2. \(v= \sqrt{v_{1} v_{2}}\)
3. \(v = \frac{v_{1} v_{2}}{v_{1} + v_{2}}\)
4. \(v=\frac{\sqrt{2} v_{1} v_{2}}{v_{1} + v_{2}}\)
A boat moves with a speed of \(5\) km/h relative to water in a river flowing with a speed of \(3\) km/h. Width of the river is \(1\) km. The minimum time taken for a round trip will be:
1. \(5\) min
2. \(60\) min
3. \(20\) min
4. \(30\) min
A river is flowing from \(W\) to \(E\) with a speed of \(5\) m/min. A man can swim in still water with a velocity of \(10\) m/min. In which direction should the man swim so as to take the shortest possible path to go to the south:
1. | \(30^{\circ}\) with downstream |
2. | \(60^{\circ}\) with downstream |
3. | \(120^{\circ}\) with downstream |
4. | South |
Certain neutron stars are believed to be rotating at about \(1\) rev/s. If such a star has a radius of \(20\) km, the acceleration of an object on the equator of the star will be:
1. | \(20 \times 10^8 ~\text{m/s}^2\) | 2. | \(8 \times 10^5 ~\text{m/s}^2\) |
3. | \(120 \times 10^5 ~\text{m/s}^2\) | 4. | \(4 \times 10^8 ~\text{m/s}^2\) |
In \(1.0~\text{s}\), a particle goes from point \(A\) to point \(B\), moving in a semicircle of radius \(1.0~\text{m}\) (see figure). The magnitude of the average velocity is:
1. | \(3.14~\text{m/s}\) | 2. | \(2.0~\text{m/s}\) |
3. | \(1.0~\text{m/s}\) | 4. | zero |
The angle turned by a body undergoing circular motion depends on the time as given by the equation, \(\theta = \theta_{0} + \theta_{1} t + \theta_{2} t^{2}\). It can be deduced that the angular acceleration of the body is?
1. \(\theta_1\)
2. \(\theta_2\)
3. \(2\theta_1\)
4. \(2\theta_2\)
A particle is moving eastwards with velocity of \(5\) m/s. In \(10\) seconds the velocity changes to \(5\) m/s northwards. The average acceleration in this time is?
1. | zero |
2. | \(\frac{1}{\sqrt{2}}~ \text{m/s}^2\) toward north-west |
3. | \(\frac{1}{\sqrt{2}}~\text{m/s}^2\) toward north-east |
4. | \(\frac{1}{2}~\text{m/s}^2 \) toward north-west |
A vector is turned without a change in its length through a small angle The value of and are, respectively:
1. | \(0, ad\theta\) | 2. | \(a d\theta, 0\) |
3. | \(0,0\) | 4. | None of these |