In an experiment with a convex lens. The plot of the image distance (\(v'\)) against the object distance \(\left(\mu^{\prime}\right)\) measured from the focus gives a curve \(v^{\prime} \mu^{\prime}=225\). If all the distances are measured in \(cm\). The magnitude of the focal length of the lens is \(cm\).

The ratio of surface tensions of mercury and water is given to be \(7.5\) while the ratio of their densities is \(13.6\). Their contact angles, with glass, are close to \(135^o\) and \(0^o\), respectively. It is observed that mercury gets depressed by an amount \(h\) in a capillary tube of radius \(r_1\), while water rises by the same amount \(h\) in a capillary tube of radius \(r_2\). The ratio, \((r_1/r_2)\), is then close to

A light wave described by \(E =60 \sin \left(3 \times 10^{15}\right) t + \sin \left(12 \times 10^{15}\right)\) t] (in SI units) falls on a metal surface of work function 2.8 eV . The maximum kinetic energy of ejected photoelectron is (approximately) _________ eV .

A spherical body of mass \(2\,kg\) starting from rest acquires a kinetic energy of \(10000\,J\) at the end of \(5^{\text {th }}\) second. The force acted on the body is \(.....N\)

A circular loop of radius \(r\) is carrying current I A. The ratio of magnetic field at the centre of circular loop and at a distance \(r\) from the center of the loop on its axis is:

Which of the following are correct expression for torque acting on a body?
A. \(\vec{\tau}=\vec{r}\times\vec{L}\)
B. \(\vec{\tau}=\frac{\mathrm{d}}{\mathrm{dt}}(\overrightarrow{\mathrm{r}} \times \overrightarrow{\mathrm{p}})\)
C. \(\vec{\tau}=\overrightarrow{\mathrm{r}} \times \frac{\mathrm{d} \mathrm{p}}{\mathrm{dt}}\)
D. \(\vec{\tau}=\mathrm{I} \vec{\alpha}\)
E. \(\vec{\tau}=\overrightarrow{\mathrm{r}} \times \overrightarrow{\mathrm{F}}\)
( \(\overrightarrow{\mathrm{r}}=\) position vector; \(\overrightarrow{\mathrm{p}}=\) linear momentum;
\(\overrightarrow{\mathrm{L}}=\) angular momentum; \(\vec{\alpha}=\) angular acceleration;
\(I=\) moment of inertia; \(\vec{F}=\) force; \(t=\) time)
Choose the correct answer from the options given below :

\(5\,g\) and radius \(1\,cm\) is fixed to a thin stick \(AB\) of negligible mass as shown in the figure. The system is initially at rest. The constant torque, that will make the system rotate about \(AB\) at \(25\) rotations per second in \(5\,s\) is close to

Three capacitors of capacitances \(25 \mu \mathrm{F}, 30 \mu \mathrm{F}\) and \(45 \mu \mathrm{F}\) are connected in parallel to a supply of \(100\) \(V\). Energy stored in the above combination is \(\mathrm{E}\). When these capacitors are connected in series to the same supply, the stored energy is \(\frac{9}{\mathrm{x}} \mathrm{E}\). The value of \(x\) is _______.