Potential energy as a function of \(r\) is given by \(U=\frac{ A }{ r ^{10}}-\frac{ B }{ r ^{5}}\), where \(r\) is the interatomic distance, \(A \) and \(B\) are positive constants. The equilibrium distance between the two atoms will be

The value of current \(i_{1}\) flowing from \(A\) to \(C\) in the circuit diagram is\(.......A\)

Consider an electrical circuit containing a two way switch \(^{\prime}{S}^{\prime}\). Initially \({S}\) is open and then \({T}_{1}\) is connected to \({T}_{2} .\) As the current in \({R}=6 \,\Omega\) attains a maximum value of steady state level, \({T}_{1}\) is disconnected from \({T}_{2}\) and immediately connected to \({T}_{3} .\) Potential drop across \({r}=3\, \Omega\) resistor immediately after \(T_{1}\) is connected to \(T_{3}\) is \(....\,V.\) (Round off to the Nearest Integer)

A simple harmonic oscillator of angular frequency \(2\,rad\,s^{-1}\) is acted upon by an external force \(F = sin\,t\,N .\) If the oscillator is at rest in its equilibrium position at \(t = 0,\) its position at later times is proportional to

The stored charge in the capacitor in steady state of the following circuit is ________ \(\mu\)C.

An object is kept at rest at a distance of 3 R above the earth's surface where R is earth's radius. The minimum speed with which it must be projected so that it does not return to earth is :
(Assume \(\mathrm{M}=\) mass of earth, \(\mathrm{G}=\) Universal gravitational constant)

In parallax method for the determination of focal length of a concave mirror, the object should always be placed :

A monochromatic light of frequency \(5 \times 10^{14} \mathrm{~Hz}\) travelling through air, is incident on a medium of refractive index ' 2 '. Wavelength of the refracted light will be :

The bulk moduli of ethanol, mercury and water are given as \(0.9, 25\) and \(2 .2\) respectively in units of \(10^9\, Nm^{-2}\) . For a given value of pressure, the fractional compression in volume is \(\frac{{\Delta V}}{V}\). Which of the following statements about \(\frac{{\Delta V}}{V}\) for these three liquids is correct ?

All resistances in figure are \(1\,\Omega\) each. The value of current ' \(I\) ' is \(\frac{a}{5}\,A\). The value of \(a\) is

\(1\) mole of rigid diatomic gas performs a work of \(Q / 5\) when heat \(Q\) is supplied to it. The molar heat capacity of the gas during this transformation is \(\frac{ x R }{8},\) The value of \(x\) is \(\ldots \ldots \ldots .\) \([ K =\) universal gas constant \(]\)

The characteristic distance at which quantum gravitational effects are significant, the Planck length, can be determined from a suitable combination of the fundamental physical constants \(G, h\) and \(c\) . Which of the following correctly gives the Planck length?

A uniform rod of mass m and length \(l\) suspended by means of two identical inextensible light strings as shown in figure. Tension in one string immediately after the other string is cut, is _________.(g acceleration due to gravity)