In an experiment for determining the gravitational acceleration \(g\) of a place with the help of a simple pendulum, the measured time period square is plotted against the string length of the pendulum in the figure. What is the value of \(g\) at the place? ...... \(m/s^2\)

A plane electromagnetic wave of frequency \(20\,MHz\) propagates in free space along \(x\)-direction. At a particular space and time, \(\overrightarrow{ E }=6.6 \hat{ j } V / m\). What is \(\overrightarrow{ B }\) at this point?

Consider two infinitely large plane parallel conducting plates as shown below. The plates are uniformly charged with a surface charge density \(+\sigma\) and \(-2 \sigma\). The force experienced by a point charge +q placed at the mid point between two plates will be :

Six equal resistances are connected between points \(P, Q\) and \(R\) as shown in figure. Then net resistance will be maximum between

Two balls of same mass and carrying equal charge are hung from a fixed support of length \(l\). At electrostatic equilibrium, assuming that angles made by each thread is small, the separation, \(x\) between the balls is proportional to

A velocity selector consists of electric field \(\overrightarrow{ E }= E \hat{ k }\) and magnetic field \(\overrightarrow{ B }= B \hat{ j }\) with \(B =12 mT\). The value \(E\) required for an electron of energy \(728 eV\) moving along the positive \(x\)-axis to pass undeflected is: (Given, , ass of electron \(=9.1 \times 10^{-31} kg\) )

A cylindrical tube AB of length \(l\), closed at both ends contains an ideal gas of 1 mol having molecular weight M. The tube is rotated in a horizontal plane with constant angular velocity \( \omega \) about an axis perpendicular to AB and passing through the edge at end A. If \( P_{A} \) and \( P_{B} \) are the pressures at A and B respectively, then (Consider the temperature is same at all points in the tube)

A body is moving in a low circular orbit about a planet of mass \(M\) and radius \(R\). The radius of the orbit can be taken to be \(R\) it self. Then the ratio of the speed of this body in the orbit to the escape velocity from the planet is

Using the given \(\mathrm{P}-\mathrm{V}\) diagram, the work done by an ideal gas along the path ABCD is :

A collimated beam of light of diameter 2 mm is propagating along x -axis. The beam is required to be expanded in a collimated beam of diameter 14 mm using a system of two convex lenses. If first lens has focal length 40 mm , then the focal length of second lens is _________ mm.

Which of the following phenomena does not explain by wave nature of light? \((A)\) reflection \((B)\) diffraction \((C)\) photoelectric effect \((D)\) interference \((E)\) polarization Choose the most appropriate answer from the options given below :