A nucleus has mass number \(\alpha\) and radius \(R_{\alpha}\). Another nucleus has mass number \(\beta\) and radius \(R_{\beta}\). If \(\beta = 8\alpha\) then \(R_{\alpha}/R_{\beta}\) is :

In connection with the circuit drawn below, the value of current flowing through \(2\, k \Omega\) resistor is ............. \(\times 10^{-4} A\)

Given below are two statements : Statement \(I\) : When speed of liquid is zero everywhere, pressure difference at any two points depends on equation \(\mathrm{P}_1-\mathrm{P}_2=\rho \mathrm{g}\left(\mathrm{h}_2-\mathrm{h}_1\right)\) Statement \(II\) : In ventury tube shown \(2 \mathrm{gh}=v_1^2-v_2^2\) In the light of the above statements, choose the most appropriate answer from the options given below.

An electromagnetic wave travelling in the \(x-\) direction has frequency of \(2 \times 10^{14}\,Hz\) and electric field amplitude of \(27\,Vm^{-1}\) . From the options given below, which one describes the magnetic field for this wave ?

A wire of length \(L\) and mass per unit length \(6.0\times 10^{-3}\; \mathrm{kgm}^{-1}\) is put under tension of \(540\; \mathrm{N}\). Two consecutive frequencies that it resonates at are : \(420\; \mathrm{Hz}\) and \(490 \;\mathrm{Hz}\). Then \(\mathrm{L}\) in meters is

A spherical soap bubble of radius \(3\,cm\) is formed inside another spherical soap bubble of radius \(6\,cm\). If the internal pressure of the smaller bubble of radius \(3\,cm\) in the above system is equal to the internal pressure of the another single soap bubble of radius \(r\,cm\). The value of \(r\) is.......

The rain drop of mass \(1\) g, starts with zero velocity from a height of \(1\) km. It hits the ground with a speed of \(5\) m/s. The work done by the unknown resistive force is _______ J. (take \(g = 10\) m/s\(^2\))

When radiation of wavelength \(\lambda\) is used to illuminate a metallic surface, the stopping potential is \(V.\) When the same surface is illuminated with radiation of wavelength \(3 \lambda,\) the stopping potential is \(\frac{ V }{4} .\) If the threshold wavelength for the metallic surface is \(n \lambda\) then value of \(n\) will be......

A conducting circular loop is placed in a uniform magnetic field of \(0.4\,T\) with its plane perpendicular to the field. Somehow, the radius of the loop starts expanding at a constant rate of \(1\,mm / s\). The magnitude of induced emf in the loop at an instant when the radius of the loop is \(2\,cm\) will be \(...........\,\mu V\).

A coil is placed perpendicular to a magnetic field of 5000 T . When the field is changed to 3000 T in 2 s , an induced emf of 22 V is produced in the coil. If the diameter of the coil is 0.02 m , then the number of turns in the coil is _______.

A person moved from \(A\) to \(B\) on a circular path as shown in figure. If the distance travelled by him is \(60 \,m\), then the magnitude of displacement would be\(.....\,m\) (Given \(\left.\cos 135^{\circ}=-0.7\right)\)