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 particle starts from the origin at t=0 and moves in the x-y plane with a constant acceleration 'a' in the y direction. Its equation of motion is . The x component of its velocity (at t=0) will be:
1. variable
2.
3.
4.
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 |
A particle is moving such that its position coordinates \((x,y)\) are \((2\) m, \(3\) m) at time \(t=0,\) \((6\) m, \(7\) m) at time \(t=2\) s and \((13\) m, \(14\) m) at time \(t=5\) s. Average velocity vector \((v_{avg})\) from \(t=0\) to \(t=5\) s is:
1. | \(\frac{1}{5}\left ( 13\hat{i}+14\hat{j} \right )\) | 2. | \(\frac{7}{3}\left ( \hat{i}+\hat{j} \right )\) |
3. | \(2\left ( \hat{i}+\hat{j} \right )\) | 4. | \(\frac{11}{5}\left ( \hat{i}+\hat{j} \right )\) |