If \(n\) represents the actual number of deflections in a converted galvanometer of resistance \(G\) and shunt resistance \(S\). Then the total current I when its figure of merit is \(K\) will be

A small particle moves to position \(5 \hat{i}-2 \hat{j}+\hat{k}\) from its initial position \(2 \hat{i}+3 \hat{j}-4 \hat{k}\) under the action of force \(5 \hat{i}+2 \hat{j}+7 \hat{k} N\). The value of work done will be \(............J\).

A physical quantity C is related to four other quantities \(\mathrm{p}, \mathrm{q}, \mathrm{r}\) and s as follows \(\mathrm{C}=\frac{\mathrm{pq}^2}{\mathrm{r}^3 \sqrt{\mathrm{~s}}}\)
The percentage errors in the measurement of \(\mathrm{p}, \mathrm{q}, \mathrm{r}\) and s are \(1 \%, 2 \% 3 \%\) and \(2 \%\) respectively. The percentage error in the measurement of C will be _____\(\%\).

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

An alternating current is represented by the equation, \(i=100 \sqrt{2} \sin (100 \pi t)\) ampere. The RMS value of current and the frequency of the given alternating current are ________.

Consider a thin metallic sheet perpendicular to the plane of the paper moving with speed \('v'\) in a uniform magnetic field \(B\) going into the plane of the paper (See figure). If charge densities \({\sigma _1}\) and \({\sigma _2}\) are induced on the left and right surfaces, respectively, of the sheet then (ignore fringe effects)

A small bulb is placed at the bottom of a tank containing water to a depth of \(\sqrt{7} \; m\). The refractive index of water is \(\frac{4}{3}\). The area of the surface of water through which light from the bulb can emerge out is \(x \,\pi m ^{2}\). The value of \(x\) is ...............

If one were to apply Bohr model to a particle of mass \('m'\) and charge \('q'\) moving in a plane under the influence of a magnetic field \('B',\) the energy of the charged particle in the \(n^{th}\) level will be

A capacitor of capacitance \(900\,\mu F\) is charged by a \(100\,V\) battery. The capacitor is disconnected from the battery and connected to another uncharged identical capacitor such that one plate of uncharged capacitor connected to positive plate and another plate of uncharged capacitor connected to negative plate of the charged capacitor. The loss of energy in this process is measured as \(x \times 10^{-2}\,J\). The value of \(x\) is \(..............\)

Two charges, each equal to \(q\), are kept at \(x = -a\) and \(x = a\) on the \(x-\)axis. A particle of mass \(m\) and charge \(q_0=\frac{q}{2}\) is placed at the origin. If charge \(q_0\) is given a small displacement \((y < < a)\) along the \(y-\)axis, the net force acting on the particle is proportional to

The bob of a pendulum was released from a horizontal position. The length of the pendulum is \(10 \mathrm{~m}\). If it dissipates \(10 \%\) of its initial energy against air resistance, the speed with which the bob arrives at the lowest point is : _______. [Use, \(\mathrm{g}: 10 \mathrm{~ms}^{-2}\) ]

An inductor coil stores \(64\, {J}\) of magnetic field energy and dissipates energy at the rate of \(640\, {W}\) when a current of \(8\, {A}\) is passed through it. If this coil is joined across an ideal battery, find the time constant of the circuit in seconds

A parallel plate capacitor having capacitance \(12\, pF\) is charged by a battery to a potential difference of \(10\, V\) between its plates. The charging battery is now disconnected and a porcelain slab of dielectric constant \(6.5\) is slipped between the plates. The work done by the capacitor on the slab is.......\(pJ\)