As shown in the figure, a block is placed in front of a convex lens. Choose the most appropriate image of the block from the following options:





Step 1: The image formation by a convex lens depends on the object's position relative to the focal point and the lens. - If the object is placed between the focus and the lens, the image formed will be virtual, upright, and magnified.
- If the object is placed beyond twice the focal length, the image formed will be real, inverted, and diminished.
Step 2: In this case, the block is placed in front of the convex lens at a distance beyond \( 2F \) (twice the focal length), so the image formed will be real, inverted, and diminished.
Step 3: According to the given options, the image that fits the description of a real, inverted, and diminished image is Option 2.
Inductance of a coil with \(10^4\) turns is \(10\,\text{mH}\) and it is connected to a DC source of \(10\,\text{V}\) with internal resistance \(10\,\Omega\). The energy density in the inductor when the current reaches \( \left(\frac{1}{e}\right) \) of its maximum value is \[ \alpha \pi \times \frac{1}{e^2}\ \text{J m}^{-3}. \] The value of \( \alpha \) is _________.
\[ (\mu_0 = 4\pi \times 10^{-7}\ \text{TmA}^{-1}) \]
\(XPQY\) is a vertical smooth long loop having a total resistance \(R\), where \(PX\) is parallel to \(QY\) and the separation between them is \(l\). A constant magnetic field \(B\) perpendicular to the plane of the loop exists in the entire space. A rod \(CD\) of length \(L\,(L>l)\) and mass \(m\) is made to slide down from rest under gravity as shown. The terminal speed acquired by the rod is _______ m/s. 