| 1. | \(90^{\circ}\) |
| 2. | \(180^{\circ}\) |
| 3. | \(0^{\circ}\) |
| 4. | equal to the angle of incidence |
A solid cylinder of mass \(2~\text{kg}\) and radius \(4~\text{cm}\) is rotating about its axis at the rate of \(3~\text{rpm}.\) The torque required to stop after \(2\pi\) revolutions is:
1. \(2\times 10^6~\text{N-m}\)
2. \(2\times 10^{-6}~\text{N-m}\)
3. \(2\times 10^{-3}~\text{N-m}\)
4. \(12\times 10^{-4}~\text{N-m}\)
The correct Boolean operation represented by the circuit diagram given above is:
1. \(\mathrm{NOR}\)
2. \(\mathrm{AND}\)
3. \(\mathrm{OR}\)
4. \(\mathrm{NAND}\)
| 1. | \(\dfrac{3}{2}mgR\) | 2. | \(mgR\) |
| 3. | \(2mgR\) | 4. | \(\dfrac{1}{2}mgR\) |
A hollow metal sphere of radius \(R\) is uniformly charged. The electric field due to the sphere at a distance \(r\) from the centre:
| 1. | decreases as \(r\) increases for \(r<R\) and for \(r>R\). |
| 2. | increases as \(r\) increases for \(r<R\) and for \(r>R\). |
| 3. | is zero as \(r\) increases for \(r<R\), decreases as \(r\) increases for \(r>R\). |
| 4. | is zero as \(r\) increases for \(r<R\), increases as \(r\) increases for \(r>R\). |
The radius of the circle, the period of revolution, initial position and direction of revolution are indicated in the figure.
The \(y\)-projection of the radius vector of rotating particle \(P\) will be:
| 1. | \(y(t)=3 \cos \left(\dfrac{\pi \mathrm{t}}{2}\right)\), where \(y\) in m |
| 2. | \(y(t)=-3 \cos 2 \pi t\) , where \(y\) in m |
| 3. | \(y(t)=4 \sin \left(\dfrac{\pi t}{2}\right)\), where \(y\) in m |
| 4. | \(y(t)=3 \cos \left(\dfrac{3 \pi \mathrm{t}}{2}\right) \), where \(y\) in m |
| 1. | \(\dfrac{1}{2}MgL\) | 2. | \(Mgl\) |
| 3. | \(MgL\) | 4. | \(\dfrac{1}{2}Mgl\) |
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. | \(10~\text{rad/s}\) |
| 1. | isochoric | 2. | isothermal |
| 3. | adiabatic | 4. | isobaric |
| 1. | \(6.4\times10^{-6}~\text{m}^{3}/\text{s}\) | 2. | \(12.6\times10^{-6}~\text{m}^{3}/\text{s}\) |
| 3. | \(8.9\times10^{-6}~\text{m}^{3}/\text{s}\) | 4. | \(2.23\times10^{-6}~\text{m}^{3}/\text{s}\) |
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