A uniform sphere of weight \(W\) and radius \(5\, cm\) is being held by a string as shown in the figure. The tension in the string will be

Two cells are connected between points \(A\) and \(B\) as shown. Cell \(1\) has emf of \(12\,V\) and internal resistance of \(3\,\Omega\). Cell \(2\) has emf of \(6\,V\) and internal resistance of \(6\,\Omega\). An external resistor \(R\) of \(4\,\Omega\) is connected across \(A\) and \(B\). The current flowing through \(R\) will be \(.............A\).

The magnitude of torque on a particle of mass \(1\,kg\) is \(2.5\, Nm\) about the origin. If the force acting on it is \(1\,N\), and the distance of the particle from the origin is \(5\,m\), the angle between the force and the position vector is (in radians)

The electric field of a plane electromagnetic wave is given by \(\overrightarrow{\mathrm{E}}=\mathrm{E}_{0} \frac{\hat{\mathrm{i}}+\hat{\mathrm{j}}}{\sqrt{2}} \cos (\mathrm{kz}+\omega \mathrm{t})\) At \(\mathrm{t}=0,\) a positively charged particle is at the point \((\mathrm{x}, \mathrm{y}, \mathrm{z})=\left(0,0, \frac{\pi}{\mathrm{k}}\right) .\) If its instantaneous velocity at \((t=0)\) is \(v_{0} \hat{\mathrm{k}},\) the force acting on it due to the wave is

In interference experiment the path difference between two interfering waves at a point \(A\) on the screen is \(\lambda/3\), where \(\lambda\) is the wavelength of these waves, and at another point \(B\) the path difference is \(\lambda/6\). The ratio of intensities at points \(A\) and \(B\) is _______.

A source of potential difference \(V\) is connected to the combination of two identical capacitors as shown in the figure. When key ' \(K\) ' is closed, the total energy stored across the combination is \(E _{1}\). Now key ' \(K\) ' is opened and dielectric of dielectric constant 5 is introduced between the plates of the capacitors. The total energy stored across the combination is now \(E _{2}\). The ratio \(E _{1} / E _{2}\) will be :

Two identical circular wires of radius \(20\,cm\) and carrying current \(\sqrt{2}\,A\) are placed in perpendicular planes as shown in figure. The net magnetic field at the centre of the circular wire is \(.............\times 10^{-8}\,T\). (Take \(\pi=3.14\) )

A body weights \(49\,N\) on a spring balance at the north pole. ..... \(N\) will be its weight recorded on the same weighing machine, if it is shifted to the equator? (Use \(g=\frac{G M}{R^{2}}=9.8 \,ms ^{-2}\) and radius of earth, \(R =6400\, km .]\)

The resistance \(R =\frac{ V }{ I },\) where \(V =(50 \pm 2) \;V\) and \(I=(20 \pm 0.2)\;A.\) The percentage error in \(R\) is \(x\%\). The value of \(x\) to the nearest integer is .........