To determine the resistance (\(R\)) of a wire, a circuit is designed below, The \(V-I\) characteristic curve for this circuit is plotted for the voltmeter and the ammeter readings as shown in figure. The value of \(\mathrm{R}\) is _______\(\Omega\).

In a resonance tube experiment when the tube is filled with water up to height of \(17.0\, cm\) from bottom, it resonates with a given tuning fork. When the water level is raised the next resonance with the same tuning fork occurs at a height of \(24.5\, cm\). If the velocity of sound in air is \(330\, m / s ,\) the tuning fork frequency is\(......Hz\)

The energy \(E\) and momentum \(p\) of a moving body of mass \(m\) are related by some equation. Given that c represents the speed of light, identify the correct equation.

A simple pendulum is being used to determine the value of gravitational acceleration \(\mathrm{g}\) at a certain place. The length of the pendulum is \(25.0\; \mathrm{cm}\) and a stop watch with \(1\; \mathrm{s}\) resolution measures the time taken for \(40\) oscillations to be \(50\; s\). The accuracy in \(g\) is  ....... \(\%\)

The escape velocity of a body on a planet  \('A'\)  is \(12 \,kms ^{-1}\). The escape velocity of the body on another planet  \('B'\) , whose density is four times and radius is half of the planet  \('A'\), is ................... \(kms ^{-1}\)

The magnetic field \(B\) crossing normally a square metallic plate of area \(4\,m ^2\) is changing with time as shown in figure. The magnitude of induced \(emf\) in the plate during \(t=2\,s\) to \(t=4\,s\), is \(..........\,mV\)

A bullet looses \({\left( {\frac{1}{n}} \right)^{th}}\) of its velocity passing through one plank. The number of such planks that are required to stop the bullet can be

Two persons pull a wire towards themselves. Each person exerts a force of \(200 \mathrm{~N}\) on the wire. Young's modulus of the material of wire is \(1 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}\). Original length of the wire is \(2 \mathrm{~m}\) and the area of cross section is \(2 \mathrm{~cm}^2\). The wire will extend in length by _______ \(\mu \mathrm{m}\).

An electric charge \(10^{-6} \mu \mathrm{C}\) is placed at origin \((0,0)\) \(\mathrm{m}\) of \(\mathrm{X}-\mathrm{Y}\) co-ordinate system. Two points \(\mathrm{P}\) and \(\mathrm{Q}\) are situated at \((\sqrt{3}, \sqrt{3}) \mathrm{m}\) and \((\sqrt{6}, 0) \mathrm{m}\) respectively. The potential difference between the points \(P\) and \(Q\) will be :

You are asked to design a shaving mirror assuming that a person keeps it \(10\,cm\) from his face and views the magnified image of the face at the closest comfortable distance of \(25\,cm.\) The radius of curvature of the mirror would then be.....\(cm\)

Angular momentum of a single particle moving with constant speed along circular path: