The force required to stretch a wire of crosssection \(1 cm ^{2}\) to double its length will be ........ \( \times 10^{7}\,N\) (Given Yong's modulus of the wire \(=2 \times 10^{11}\,N / m ^{2}\) )

\(1\,\mu\)C charge moving with velocity \(\vec{v} = \left(\hat{i} - 2\hat{j} + 3\hat{k}\right)\) m/s in the region of magnetic field \(\vec{B} = \left(2\hat{i} + 3\hat{j} - 5\hat{k}\right)\) T. The magnitude of force acting on it is \(\sqrt{\alpha} \times 10^{-6}\) N. The value of \(\alpha\) is _______.

A particle is executing simple harmonic motion \((SHM)\) of amplitude \(A,\) along the \(x-\) axis, about \(x = 0.\) When its potential energy \((PE)\) equals kinetic energy \((KE),\) the position of the particle will be

Given below are two statements : \(Statement\) \((I)\) : Planck's constant and angular momentum have same dimensions. \(Statement\) \((II)\) : Linear momentum and moment of force have same dimensions. In the light of the above statements, choose the correct answer from the options given below :

A \(0.07\,{H}\) inductor and a \(12 \,\Omega\) resistor are connected in series to a \(220 \,{V}, 50 \,{Hz}\) ac source. The approximate current in the circuit and the phase angle between current and source voltage are respectively. [Take \(\pi\) as \(\left.\frac{22}{7}\right]\)

There are three co-centric conducting spherical shells \(A , B\) and C of radii \(a , b\) and c respectively. The potential of the spheres \(A , B\) and C respectively, are :

The coercivity of a magnet is \(5 \times 10^3 \mathrm{~A} / \mathrm{m}\). The amount of current required to be passed in a solenord of length \(30 \mathrm{~cm}\) and the number of turns \(150\) , so that the magnet gets demagnetised when inside the solenoid is _______ A.

A convex lens (of focal length \(20\, cm\)) and a concave mirror, having their principal axes along the same lines, are kept \(80\, cm\) apart from each other. The concave mirror is to the right of the convex lens. When an object is kept at a distance of \(30\, cm\) to the left of the convex lens, its image remains at the same position even if the concave mirror is removed. The maximum distance of the object for which this concave mirror, by itself would produce a virtual image would be.....\(cm\)

A cylindrical vessel containing a liquid is rotated about its axis so that the liquid rises at its sides as shown in the figure. The radius of vessel is \(5\, cm\) and the angular speed of rotation is  \(\omega\; rad \,s^{-1}\). The difference in the height, \(h(\) in \(cm )\) of liquid at the centre of vessel and at the side will be

Three charges \(Q, +q\) and \(+q\) are placed at the vertices of a right -angle isosceles triangle as shown below. The net electrostatic energy of the configuration is zero, if the value of \(Q\) is

The total internal energy of two mole monoatomic ideal gas at temperature \(T=300\,K\) will be ...........\(J\). \(\text { (Given } R =8.31\,J / mol.K )\)