A pendulum is suspended by a string of length \(250\,cm\). The mass of the bob of the pendulum is \(200\,g\). The bob is pulled aside until the string is at \(60^{\circ}\) with vertical as shown in the figure. After releasing the bob. the maximum velocity attained by the bob will be________ \(ms ^{-1}\). (if \(g=10\,m / s ^{2}\) )

In an experiment for estimating the value of focal length of converging mirror, image of an object placed at \(40\,cm\) from the pole of the mirror is formed at distance \(120\,cm\) from the pole of the mirror. These distances are measured with a modified scale in which there are \(20\) small divisions in \(1\,cm\). The value of error in measurement of focal length of the mirror is \(1 / K\) \(cm\). The value of \(K\) is  \(..........\)

A circular disc of mass \(M\) and radius \(R\) is rotating about its axis with angular speed \(\omega_{1}\) If another stationary disc having radius \(\frac{ R }{2}\) and same mass \(M\) is dropped co-axially on to the rotating disc. Gradually both discs attain constant angular speed \(\omega_{2}\). The energy lost in the process is \(p \%\) of the initial energy. Value of \(p\) is

Paramagnetic substances: \(A\). align themselves along the directions of external magnetic field. \(B\). attract strongly towards external magnetic field. \(C\). has susceptibility little more than zero. \(D\). move from a region of strong magnetic field to weak magnetic field. Choose the most appropriate answer from the options given below:

The volume of an ideal gas increases 8 times and temperature becomes (1/4) of initial temperature during a reversible change. If there is no exchange of heat in this process (\( \Delta Q=0 \)) then identify the gas from the following options:

A magnetic dipole in a constant magnetic field has 

A galvanometer with its coil resistance \(25\,\Omega \) requires a current of  \(1\,mA\)  for its full deflection. In order to construct an ammeter to read up to a current of \(2\,A,\)  the approximate value of the shunt resistance should be

An average force of \(125\,N\) is applied on a machine gun firing bullets each of mass \(10\,g\) at the speed of \(250\,m / s\) to keep it in position. The number of bullets fired per second by the machine gun is:

An electromagnetic wave travels in free space along the \(x\)-direction. At a particular point in space and time, \(\vec{B} = 2 \times 10^{-7} \hat{j}\) T is associated with this wave. The value of corresponding electric field \(\vec{E}\) at this point is _______ V/m.

Given below are two statements: Statement \(I:\) If heat is added to a system, its temperature must increase. Statement \(II:\) If positive work is done by a system in a thermodynamic process, its volume must increase. In the light of the above statements, choose the correct answer from the options given below