In the given figure, there is a circuit of potentiometer of length \(A B=10 \,{m}\). The resistance per unit length is \(0.1 \,\Omega\) per \({cm}\). Across \({AB}\), a battery of emf \({E}\) and internal resistance ' \({r}^{\prime}\) is connected. The maximum value of emf measured by this potentiometer is : (In \(V\))

If \(\lambda_{1}\) and \(\lambda_{2}\) are the wavelengths of the third member of Lyman and first member of the Paschen series respectively, then the value of \(\lambda_{1}: \lambda_{2}\) is

A body of mass \(m= 10^{-2}\) \(kg\) is moving in a medium and experiences a frictional force \(F= -kv^2\). Its initial speed is \(v_0= 10\) \(ms^{-1}\). If, after \(10\; s\), its energy is \(\frac{1}{8}\) \(mv_0^2\) the value of \(k\) will be

A body of mass 1 kg is suspended with the help of two strings making angles as shown in figure. Magnitude of tensions \(T_1\) and \(T_2\), respectively, are (in N) :

Figure below shows a liquid being pushed out of the tube by a piston having area of cross section \(2.0\,cm ^2\). The area of cross section at the outlet is \(10\,mm ^2\). If the piston is pushed at a speed of \(4\,cm s ^{-1}\), the speed of outgoing fluidis \(.........\,cm s ^{-1}\).

A simple pendulum of length \(1\, m\) is oscillating with an angular frequency \(10\, rad/s\). The support of the pendulum starts oscillating up and down with a small angular frequency of \(1\, rad/s\) and an amplitude of \(10^{-2}\, m\). The relative change in the angular frequency of the pendulum is best given by

Two resistance of \(100\ \Omega\) and \(200\  \Omega\) are connected in series with a battery of \(4 \mathrm{~V}\) and negligible internal resistance. \(A\) voltmeter is used to measure voltage across \(100 \Omega\) resistance, which gives reading as \(1 \mathrm{~V}\). The resistance of voltmeter must be _______ \(\Omega\).

A parallel plate capacitor with plate area \('A'\) and distance of separation \('d'\) is filled with a dielectric. What is the capacity of the capacitor when permittivity of the dielectric varies as : \(\varepsilon(x)=\varepsilon_{0}+k x, \text { for }\left(0\,<\,x \leq \frac{d}{2}\right)\) \(\varepsilon(x)=\varepsilon_{0}+k(d-x)\), for \(\left(\frac{d}{2} \leq x \leq d\right)\)

The displacement current of \(4.425 \,\mu A\) is developed in the space between the plates of parallel plate capacitor when voltage is changing at a rate of \(10^{6} \,Vs ^{-1}\). The area of each plate of the capacitor is \(40 \,cm ^{2}\). The distance between each plate of the capacitor is \(x \times 10^{-3} \,m\). The value of \(x\) is ................ (Permittivity of free space, \(\varepsilon _{0}=8.85 \times 10^{-12} \,C ^{2} N ^{-1} m ^{-2}\) )

An electric dipole of mass m, charge q, and length \(l\) is placed in a uniform electric field \(\overrightarrow{\mathrm{E}}=\mathrm{E}_0 \hat{i}\). When the dipole is rotated slightly from its equilibrium position and released, the time period of its oscillations will be:

A particle of mass \(m\) is moving in a circular path of constant radius \(I\) such that its centripetal acceleration \((a)\) is varying with time \(t\) as \(a=k^{2} rt^{2}\). where \(k\) is a constant. The 10.Power delivered to the particle by the force acting on it is given as

The general displacement of a simple harmonic oscillator is \(x = A \sin \omega t\). Let \(T\) be its time period. The slope of its potential energy (U) - time (t) curve will be maximum when \(t=\frac{T}{\beta}\). The value of \(\beta\) is \(.........\)

The eye can be regarded as a single refracting surface. The radius of curvature of this surface is equal to that of cornea \((7.8\, mm)\). This surface separates two media of refractive indices \(1\) and \(1.34\). Calculate the distance from the refracting surface at which a parallel beam of light will come to focus.......\(cm\)