A convex lens of refractive index \(1.5\) and focal length \(18 cm\) in air is immersed in water. The change in focal length of the lens will be \(...........cm\).\(\left(\right.\) Given refractive index of water \(\left.=\frac{4}{3}\right)\)

Consider a cylinder of mass \(M\) resting on a rough horizontal rug that is pulled out from under it with acceleration \('a'\) perpendicular to the axis of the cylinder. What is \(F_{friction}\) at point \(P\) ? It is assumed that the cylinder does not slip

A tuning fork resonates with a sonometer wire of length \(1 \mathrm{~m}\) stretched with a tension of \(6 \mathrm{~N}\). When the tension in the wire is changed to \(54 \mathrm{~N}\), the same tuning fork produces \(12\) beats per second with it. The frequency of the tuning fork is _______ \(\mathrm{Hz}\).

The minimum frequency of photon required to break a particle of mass 15.348 amu into 4\( \alpha \) particles is __________ kHz.
[mass of He nucleus = 4.002 amu,
\(1 amu =1.66 \times 10^{-27} kg, h =6.6 \times 10^{-34} J . s\) and \(c =\) \(\left.3 \times 10^8 m / s \right]\)

A current through a wire depends on time as \(i =\alpha_{0} t +\beta t ^{2}\) where \(\alpha_{0}=20 A / s\) and \(\beta=8 As ^{-2} .\) Find the charge crossed through a section of the wire in \(15 \,s\) (in \(C\))

A particle is released from height \(S\) above the surface of the earth. At certain height its kinetic energy is three times its potential energy. The height from the surface of the earth and the speed of the particle at that instant are respectively.

Two charges \(q\) and \(3 q\) are separated by a distance ' \(r\) ' in air. At a distance \(x\) from charge \(q\), the resultant electric field is zero. The value of \(x\) is _______.

Given below are two statements : Statement \(I :\) Stopping potential in photoelectric effect does not depend on the power of the light source. Statement \(II :\) For a given metal, the maximum kinetic energy of the photoelectron depends on the wavelength of the incident light. In the light of above statements, choose the most appropriate answer from the options given below. Options :

A \(5\) mg particle carrying a charge of \(5\pi\times 10^{-6}\) C is moving with velocity of \((3\hat{i}+2\hat{k})\times 10^{-2}\) m/s in a region having magnetic field \(\vec{B} = 0.1\hat{k}\) Wb/m\(^2\). It moves a distance of \(\alpha\) meter along \(\hat{k}\) when it completes \(5\) revolutions. The value of \(\alpha\) is ________.

A uniform cylinder of length \(L\) and mass \(M\) having cross-sectional area \(A\) is suspended, with its length vertical, from a fixed point by a massless spring, such that it is half submerged in a liquid of density \(\sigma \) at equilibrium position. When the cylinder is given a downward push and released, it starts oscillating vertically with a small amplitude. The time period \(T\) of the oscillations of the cylinder will be