Eight copper wire of length \(l\) and diameter \(d\) are joined in parallel to form a single composite conductor of resistance \(R\). If a single copper wire of length \(2\,l\) have the same resistance \((R)\) then its diameter will be \(.....d\).

A magnetic field vector in an electromagnetic wave is represented by \(\vec{B}=B_0\sin\left(2\pi vt-\dfrac{2\pi x}{\lambda}\right)\hat{j}\). Its associated electric field vector is ______.

A telescope with objective diameter \(R\) is used to observe a distant star emitting light of wavelength \(500\) nm, at a resolution of \(5 \times 10^{-7}\) radian. The value of \(R\) is _____ cm.

Two cells of same emf but different internal resistances \(I_{1}\) and \(I_{2}\) are connected in series with a resistance \(R\). The value of resistance \(R\), for which the potential difference across second cell is zero, is

What equal length of an iron wire and a copper-nickel alloy wire, each of \(2 \; {mm}\) diameter connected parallel to give an equivalent resistance of \(3 \Omega ?\) (Given resistivities of iron and copper-nickel alloy wire are \(12 \;\mu \Omega {cm}\) and \(51\; \mu \Omega {cm}\) respectively) (in \({m}\))

The momentum of a body is increased by \(50 \%\). The percentage increase in the kinetic energy of the body is \(...........\,\%\)

In the Bohr 's model of hydrogen-like atom the force between the nucleus and the electron is modified as \(F = \frac{{{e^2}}}{{4\pi {\varepsilon _0}}}\left( {\frac{1}{{{r^2}}} + \frac{\beta }{{{r^3}}}} \right)\), where \(\beta \) is a constant. For this atom, the radius of the \(n^{th}\) orbit in terms of the Bohr radius \(\left( {{a_0} = \,\frac{{{\varepsilon _0}{h^2}}}{{m\pi {e^2}}}} \right)\) is

A sinusoidal voltage of peak value \(283\, V\) and angular frequency \(320/s\) is applied to a series \(LCR\) circuit. Given that \(R\, = 5\,\Omega \) , \(L\,= 25\, mH\) and \(C\, = 1000\, \mu F\). The total impedance, and phase difference between the voltage across the source and the current will respectively be

A bi convex lens of focal length \(10\,cm\) is cut in two identical parts along a plane perpendicular to the principal axis. The power of each lens after cut is \(...........\,D\).

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : Time period of a simple pendulum is longer at the top of a mountain than that at the base of the mountain.
Reason (R): Time period of a simple pendulum decreases with increasing value of acceleration due to gravity and vice-versa.
In the light of the above statements, choose the most appropriate answer from the options given below :

Dimension of \(\frac{1}{\mu_0 \varepsilon_0}\) should be equal to