Which of the following pair of nuclei are isobars of the element?

A uniform thin rope of length \(12\, m\) and mass \(6\, kg\) hangs vertically from a rigid support and a block of mass \(2\, kg\) is attached to its free end. A transverse short wavetrain of wavelength \(6\, cm\) is produced at the lower end of the rope. What is the wavelength of the wavetrain (in \(cm\) ) when it reaches the top of the rope \(?\)

A system of three polarizers \(P_1, P_2, P_3\) is set up such that the pass axis of \(P_3\) is crossed with respect to that of \(P_1\). The pass axis of \(P_2\) is inclined at \(60^o\) to the pass axis of \(P_3\). When a beam of unpolarized light of intensity \(I_0\) is incident on \(P_1\), the intensity of light transmitted by the three polarizers is \(I\). The ratio \((I_0/I)\) equals (nearly)

In Millikan's oil drop experiment, what is viscous force acting on an uncharged drop of radius \(2.0 \times 10^{-5}\, {m}\) and density \(1.2 \times 10^{3} \,{kgm}^{-3}\) ? Take viscosity of liquid \(=1.8 \times 10^{-5}\, {Nsm}^{-2} .\) (Neglect buoyancy due to air).

In a coil of resistance \(100\ \Omega\) , a current is induced by changing the magnetic flux through it as shown in the figure. The magnitude of change in flux through the coil is......\(Wb\)

If \(\mathrm{n}\) is the number density and \(\mathrm{d}\) is the diameter of the molecule, then the average distance covered by a molecule between two successive collisions (i.e. mean free path) is represented by _______.

The radiation corresponding to \(3 \rightarrow 2\) transition of a hydrogen atom falls on a gold surface to generate photoelectrons. These electrons are passed through a magnetic field of \(5 \times 10^{-4} \,{T}\). Assume that the radius of the largest circular path followed by these electrons is \(7\, {mm}\), the work function of the metal is \(.....\,{eV}\) (Mass of electron \(=9.1 \times 10^{-31} \,{kg}\) )

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:

The de Broglie wavelength for an electron accelerated through the potential difference of \(V_1\) volt is \(\lambda_1\). When the potential difference is changed to \(V_2\) volt, the associated de Broglie wavelength is increased by \(50\%\). If \((V_1/V_2) = (9/\alpha)\), then the value of \(\alpha\) is __________.

Light enters from air into a given medium at an angle of \(45^{\circ}\) with interface of the air-medium surface. After refraction, the light ray is deviated through an angle of \(15^{\circ}\) from its original direction. The refractive index of the medium is.

Given below are two statements: Statement \(I :\) Maximum power is dissipated in a circuit containing an inductor, a capacitor and a resistor connected in series with an \(AC\) source, when resonance occurs Statement \(II :\) Maximum power is dissipated in a circuit containing pure resistor due to zero phase difference between current and voltage. In the light of the above statements, choose the correct answer from the options given below :

The energy required to take a satellite to a height \(‘h’\) above Earth surface (radius of Earth \(= 6.4 \times 10^3\,km\) ) is \(E_1\) and kinetic energy required for the satellite to be in a circular orbit at this height is \(E_2.\) The value of \(h\) for which \(E_1\) and \(E_2\) are equal is

An infinite plane sheet of charge having uniform surface charge density \(+\sigma_5 \mathrm{C} / \mathrm{m}^2\) is placed on \(\mathrm{x}-\mathrm{y}\) plane. Another infinitely long line charge having uniform linear charge density \(+\lambda_e \mathrm{C} / \mathrm{m}\) is placed at \(z=4 \mathrm{~m}\) plane and parallel to \(y\)-axis. If the magnitude values \(\left|\sigma_s\right|=2\left|\lambda_{\mathrm{e}}\right|\) then at point \((0,0,2)\), the ratio of magnitudes of electric field values due to sheet charge to that of line charge is \(\pi \sqrt{\mathrm{n}}: 1\). The value of \(n\) is _______.