A block of mass \(10~\text{kg}\) is in contact with the inner wall of a hollow cylindrical drum of radius \(1~\text{m}.\) The coefficient of friction between the block and the inner wall of the cylinder is \(0.1.\) The minimum angular velocity needed for the cylinder, which is vertical and rotating about its axis, will be:
\(\left(g= 10~\text{m/s}^2\right )\)
| 1. | \(10~\pi~\text{rad/s}\) | 2. | \(\sqrt{10}~\pi~\text{rad/s}\) |
| 3. | \(\dfrac{10}{2\pi}~\text{rad/s}\) | 4. | \(10~\text{rad/s}\) |
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. | \(2\times 10^{-3}~\text{V}\) |
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 body weighs \(200\) N on the surface of the earth. How much will it weigh halfway down the centre of the earth?
| 1. | \(100\) N | 2. | \(150\) N |
| 3. | \(200\) N | 4. | \(250\) N |
An electron is accelerated through a potential difference of \(10,000~\text{V}\). Its de-Broglie wavelength is, (nearly):
\(\left(m_e = 9\times 10^{-31}~\text{kg}\right )\)
1. \(12.2~\text{nm}\)
2. \(12.2\times 10^{-13}~\text{m}\)
3. \(12.2\times 10^{-12}~\text{m}\)
4. \(12.2\times 10^{-14}~\text{m}\)
Two parallel infinite line charges with linear charge densities \(+\lambda~\text{C/m}\) and \(+\lambda~\text{C/m}\) are placed at a distance \({R}.\) The electric field mid-way between the two line charges is:
| 1. | \(\frac{\lambda}{2 \pi \varepsilon_0 {R}}~\text{N/C}\) | 2. | zero |
| 3. | \(\frac{2\lambda}{ \pi \varepsilon_0 {R}} ~\text{N/C}\) | 4. | \(\frac{\lambda}{ \pi \varepsilon_0 {R}}~\text{N/C}\) |
An increase in the temperature of a gas-filled container would lead to:
| 1. | decrease in intermolecular distance. |
| 2. | increase in its mass. |
| 3. | increase in its kinetic energy. |
| 4. | decrease in its pressure. |
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 |
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. | \(2~\text{J}\) |
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