| 1. | \(2:1\) | 2. | \(4:9\) |
| 3. | \(9:4\) | 4. | \(1:2\) |
A disc of radius \(2~\text{m}\) and mass \(100~\text{kg}\) rolls on a horizontal floor. Its centre of mass has a speed of \(20~\text{cm/s}\). How much work is needed to stop it?
1. \(1~\text{J}\)
2. \(3~\text{J}\)
3. \(30~\text{J}\)
4. \(2~\text{J}\)
Body \(\mathrm{A}\) of mass \(4m\) moving with speed \(u\) collides with another body \(\mathrm{B}\) of mass \(2m\) at rest. The collision is head-on and elastic in nature. After the collision, the fraction of energy lost by the colliding body \(\mathrm{A}\) is:
| 1. | \(\dfrac{5}{9}\) | 2. | \(\dfrac{1}{9}\) |
| 3. | \(\dfrac{8}{9}\) | 4. | \(\dfrac{4}{9}\) |
Two similar thin equi-convex lenses, of focal length \(f\) each, are kept coaxially in contact with each other such that the focal length of the combination is \(F_1\). When the space between the two lenses is filled with glycerin which has the same refractive index as that of glass \((\mu = 1.5),\) then the equivalent focal length is \(F_2\). The ratio \(F_1:F_2\) will be:
1. \(3:4\)
2. \(2:1\)
3. \(1:2\)
4. \(2:3\)
Then the amplitude of its oscillation is given by:
| 1. | \(A + B\) | 2. | \(A_{0}\) \(+\) \(\sqrt{A^{2} + B^{2}}\) |
| 3. | \(\sqrt{A^{2} + B^{2}}\) | 4. | \(\sqrt{A_{0}^{2}+\left( A + B \right)^{2}}\) |
Two particles \(A\) and \(B\) are moving in a uniform circular motion in concentric circles of radii \(r_A\) and \(r_B\) with speeds \(v_A\) and \(v_B\) respectively. Their time periods of rotation are the same. The ratio of the angular speed of \(A\) to that of \(B\) will be:
| 1. | \( 1: 1 \) | 2. | \(r_A: r_B \) |
| 3. | \(v_A: v_B \) | 4. | \(r_B: r_A\) |
A soap bubble, having a radius of \(1~\text{mm}\), is blown from a detergent solution having a surface tension of \(2.5\times 10^{-2}~\text{N/m}\). The pressure inside the bubble equals at a point \(Z_0\) below the free surface of the water in a container. Taking \(g = 10~\text{m/s}^{2}\), the density of water \(= 10^{3}~\text{kg/m}^3\), the value of \(Z_0\) is:
1. \(0.5~\text{cm}\)
2. \(100~\text{cm}\)
3. \(10~\text{cm}\)
4. \(1~\text{cm}\)
A \(800\) turn coil of effective area \(0.05~\text{m}^2\) is kept perpendicular to a magnetic field \(5\times 10^{-5}~\text{T}\). When the plane of the coil is rotated by \(90^{\circ}\)around any of its coplanar axis in \(0.1~\text{s}\), the emf induced in the coil will be:
| 1. | \(0.02~\text{V}\) | 2. | \(2~\text{V}\) |
| 3. | \(0.2~\text{V}\) | 4. | \(2\times 10^{-3}~\text{V}\) |
A particle moving with velocity \(\vec{v}\) is acted by three forces shown by the vector triangle \({PQR}.\) The velocity of the particle will:
| 1. | change according to the smallest force \({\overrightarrow{Q R}}\) |
| 2. | increase |
| 3. | decrease |
| 4. | remain constant |
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