A biconvex lens of focal length $f$ forms a circular image of sun of radius $r$ in focal plane. Then

Graph of position of image versus position of point object from a convex lens is shown. Then, the focal length of the lens is

A massless rod is suspended by two identical strings AB and CD of equal length. A block of mass $m$ is suspended from point $O$ such that BO is equal to $x$. Further, it is observed that the frequency of 1st harmonic (fundamental frequency) in AB is equal to 2 nd harmonic frequency in CD. Then, length of BO is

A system of binary stars of masses $m_{\mathrm{A}}$ and $m_{\mathrm{B}}$ are moving in circular orbits of radii $r_{\mathrm{A}}$ and $r_R$, respectively. If $\mathrm{T}_A$ and $\mathrm{T}_B$ are the time periods of masses $m_A$ and $m_B$ respectively, then