Two identical balls \(A\) and \(B\) having velocities of \(0.5~\text{m/s}\) and \(-0.3~\text{m/s}\), respectively, collide elastically in one dimension. The velocities of \(B\) and \(A\) after the collision, respectively, will be:
| 1. | \(-0.5~\text{m/s}~\text{and}~0.3~\text{m/s}\) |
| 2. | \(0.5~\text{m/s}~\text{and}~-0.3~\text{m/s}\) |
| 3. | \(-0.3~\text{m/s}~\text{and}~0.5~\text{m/s}\) |
| 4. | \(0.3~\text{m/s}~\text{and}~0.5~\text{m/s}\) |
A particle moves from a point \(\left(\right. - 2 \hat{i} + 5 \hat{j} \left.\right)\) to \(\left(\right. 4 \hat{j} + 3 \hat{k} \left.\right)\) when a force of \(\left(\right. 4 \hat{i} + 3 \hat{j} \left.\right)\) \(\text{N}\) is applied. How much work has been done by the force?
| 1. | \(8\) J | 2. | \(11\) J |
| 3. | \(5\) J | 4. | \(2\) J |
Two rotating bodies \(A\) and \(B\) of masses \(m\) and \(2m\) with moments of inertia \(I_A\) and \(I_B\) \(\left(I_B>I_A\right)\) have equal kinetic energy of rotation. If \(L_A\) and \(L_B\) be their angular momenta respectively, then:
1. \(L_A = \frac{L_B}{2}\)
2. \(L_A = 2L_B\)
3. \(L_B>L_A\)
4. \(L_A>L_B\)
A solid sphere of mass \(m\) and radius \(R\) is rotating about its diameter. A solid cylinder of the same mass and the same radius is also rotating about its geometrical axis with an angular speed twice that of the sphere. The ratio of their kinetic energies of rotation (sphere/cylinder) will be:
| 1. | \(2:3\) | 2. | \(1:5\) |
| 3. | \(1:4\) | 4. | \(3:1\) |
| 1. | \(\dfrac{m_1m_2}{m_1+m_2}l^2\) | 2. | \(\dfrac{m_1+m_2}{m_1m_2}l^2\) |
| 3. | \((m_1+m_2)l^2\) | 4. | \(\sqrt{(m_1m_2)}l^2\) |
Starting from the centre of the earth, having radius \(R,\) the variation of \(g\) (acceleration due to gravity) is shown by:
| 1. |  |
2. |  |
| 3. |  |
4. |  |
A satellite of mass \(m\) is orbiting the earth (of radius \(R\)) at a height \(h\) from its surface. What is the total energy of the satellite in terms of \(g_0?\)
(\(g_0\) is the value of acceleration due to gravity at the earth's surface)
| 1. | \(\dfrac{mg_0R^2}{2(R+h)}\) | 2. | \(-\dfrac{mg_0R^2}{2(R+h)}\) |
| 3. | \(\dfrac{2mg_0R^2}{(R+h)}\) | 4. | \(-\dfrac{2mg_0R^2}{(R+h)}\) |
A rectangular film of liquid is extended from \((4~\text{cm} \times 2~\text{cm})\) to \((5~\text{cm} \times 4~\text{cm}).\) If the work done is \(3\times 10^{-4}~\text J,\) then the value of the surface tension of the liquid is:
| 1. | \(0.250~\text{Nm}^{-1}\) | 2. | \(0.125~\text{Nm}^{-1}\) |
| 3. | \(0.2~\text{Nm}^{-1}\) | 4. | \(8.0~\text{Nm}^{-1}\) |
Three liquids of densities \(\rho_1,\rho_2\) and \(\rho_3\) \((\rho_1>\rho_2>\rho_3)\) having the same value of the surface tension \(T,\) rise to the same height in three identical capillaries. The angles of contact \(\theta_1,\theta_2\) and \(\theta_3\) obey:
1. \( \frac{\pi}{2}>\theta_1>\theta_2>\theta_3 \geq 0 \)
2. \( 0 \leq \theta_1<\theta_2<\theta_3<\frac{\pi}{2} \)
3. \( \frac{\pi}{2}<\theta_1<\theta_2<\theta_3<\pi \)
4. \( \pi>\theta_1>\theta_2>\theta_3>\frac{\pi}{2} \)
Two identical bodies are made of a material for which the heat capacity increases with temperature. One of these is at \(100~^{\circ}\text{C},\) while the other one is at \(0~^{\circ}\text{C}.\) If the two bodies are brought into contact, then assuming no heat loss, the final common temperature is:
| 1. | \(50~^{\circ}\text{C}\) |
| 2. | more than \(50~^{\circ}\text{C}\) |
| 3. | less than \(50~^{\circ}\text{C}\) but greater than \(0~^{\circ}\text{C}\) |
| 4. | \(0~^{\circ}\text{C}\) |
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