One end of the string of length \(l\) is connected to a particle of mass \(m\) and the other end is connected to a small peg on a smooth horizontal table. If the particle moves in a circle with speed \(v\), the net force on the particle (directed towards the center) will be: (\(T\) represents the tension in the string)
| 1. | \(T+\dfrac{m v^2}{l}\) | 2. | \(T-\dfrac{m v^2}{l}\) |
| 3. | zero | 4. | \(T\) |
A car is negotiating a curved road of radius \(R\). The road is banked at an angle \(\theta\). The coefficient of friction between the tyre of the car and the road is \(\mu_s\). The maximum safe velocity on this road is:
| 1. | \(\sqrt{\operatorname{gR}\left(\dfrac{\mu_{\mathrm{s}}+\tan \theta}{1-\mu_{\mathrm{s}} \tan \theta}\right)}\) | 2. | \(\sqrt{\frac{\mathrm{g}}{\mathrm{R}}\left(\dfrac{\mu_{\mathrm{s}}+\tan \theta}{1-\mu_{\mathrm{s}} \tan \theta}\right)}\) |
| 3. | \(\sqrt{\frac{\mathrm{g}}{\mathrm{R}^2}\left(\dfrac{\mu_{\mathrm{s}}+\tan \theta}{1-\mu_{\operatorname{s}} \tan \theta}\right)}\) | 4. | \(\sqrt{\mathrm{gR}^2\left(\dfrac{\mu_{\mathrm{s}}+\tan \theta}{1-\mu_{\mathrm{s}} \tan \theta}\right)}\) |
A rigid rod is placed against the wall as shown in the figure. When the velocity at its lower end is \(10\) ms-1 and its base makes an angle \(\alpha=60^\circ\) with horizontal, then the vertical velocity of its end \(\mathrm{B}\) (in ms-1) will be:
| 1. | \(10\sqrt{3}\) | 2. | \(\frac{10}{\sqrt{3}}\) |
| 3. | \(5\sqrt{3}\) | 4. | \(\frac{5}{\sqrt{3}}\) |
What will be the reading of the spring balance in the given setup? (take \(g=10~\text{m/s}^2\) )
1. \(60~\text N\)
2. \(40~\text N\)
3. \(50~\text N\)
4. \(80~\text N\)
A particle is observed from two frames \(S_1\) and \(S_2.\) The frame \(S_2\) moves with respect to \(S_1\) with an acceleration \(a.\) Let \(F_1\) and \(F_2\) be the pseudo forces on the particle when seen from \(S_1\) and \(S_2\) respectively. Which of the following are not possible?
1. \(F_1=0,~F_2\neq0\)
2. \(F_1\neq0,~F_2=0\)
3. \(F_1\neq0,~F_2\neq0\)
4. \(F_1=0,~F_2=0\)
| Assertion (A): | Mass of a body decreases slightly when it is negatively charged. |
| Reason (R): | Charging is due to the transfer of electrons. |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | (A) is False but (R) is True. |
| 1. | \(12\times10^{-1}\) N-m | 2. | \(12\times10^{-3}\) N-m |
| 3. | \(24\times10^{-1}\) N-m | 4. | \(24\times10^{-3}\) N-m |
An electric field is uniform, and in the positive \(x\)-direction for positive \(x\), and uniform with the same magnitude but in the negative \(x\)-direction for negative \(x\). It is given that \(\vec{E}=200\hat{i}\) N/C for \(x>0\) and \(\vec{E}=-200\hat{i}\) N/C for \(x<0\). A right circular cylinder of length \(20~\text{cm}\) and radius \(5~\text{cm}\) has its centre at the origin and its axis along the \(x\text{-}\)axis so that one face is at \(x= + 10~\text{cm}\) and the other is at \(x= -10~\text{cm}\) (as shown in the figure). What is the net outward flux through the cylinder?
1. \(0\)
2. \(1.57~\text{Nm}^2\text{C}^{-1}\)
3. \(3.14~\text{Nm}^2\text{C}^{-1}\)
4. \(2.47~\text{Nm}^2\text{C}^{-1}\)
| 1. | \(8~\text{mC}\) | 2. | \(2~\text{mC}\) |
| 3. | \(5~\text{mC}\) | 4. | \(7~\mu \text{C}\) |
A toy car with charge \(q\) moves on a frictionless horizontal plane surface under the influence of a uniform electric field \(\vec {E}.\) Due to the force \(q\vec {E},\) its velocity increases from \(0\) to \(6~\text{m/s}\) in a one-second duration. At that instant, the direction of the field is reversed. The car continues to move for two more seconds under the influence of this field. The average velocity and the average speed of the toy car between \(0\) to \(3\) seconds are respectively:
| 1. | \(2~\text{m/s}, ~4~\text{m/s}\) | 2. | \(1~\text{m/s}, ~3~\text{m/s}\) |
| 3. | \(1~\text{m/s}, ~3.5~\text{m/s}\) | 4. | \(1.5~\text{m/s},~ 3~\text{m/s}\) |
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