Wheatstone bridge principle is used to measure the specific resistance \(\left(S_1\right)\) of given wire, having length \(L\), radius \(r\). If \(X\) is the resistance of wire, then specific resistance is: \(S_1=X\left(\frac{\pi r^2}{L}\right)\). If the length of the wire gets doubled then the value of specific resistance will be :

Which is the correct ascending order of wavelengths?

The distance between object and its two times magnified real image as produced by a convex lens is \(45 \mathrm{~cm}\). The focal length of the lens used is _______ \(\mathrm{cm}\).

A body of mass \(10 kg\) is projected at an angle of \(45^{\circ}\) with the horizontal. The trajectory of the body is observed to pass through a point \((20,10)\). If \(T\) is the time of flight, then its momentum vector, at time \(t =\frac{ T }{\sqrt{2}}\), is. \(\left[\right.\) Take \(\left.g=10 m / s ^{2}\right]\)

Which statements are correct about degrees of freedom? \(A.\) \(A\) molecule with \(n\) degrees of freedom has \(n^{2}\) different ways of storing energy. \(B.\) Each degree of freedom is associated with \(\frac{1}{2} RT\) average energy per mole. \(C.\) \(A\) monoatomic gas molecule has \(1\) rotational degree of freedom where as diatomic molecule has \(2\) rotational degrees of freedom \(D\) \(CH _{4}\) has a total to \(6\) degrees of freedom Choose the correct answer from the option given below:

Moment of inertia of a cylinder of mass \(M,\) length \(L\) and radius \(R\) about an axis passing through its centre and perpendicular to the axis of the cylinder is \(I = M \left(\frac{ R ^{2}}{4}+\frac{ L ^{2}}{12}\right) .\) If such a cylinder is to be made for a given mass of material, the ratio \(\frac LR\) for it to have minimum possible \(I\) is

The distance between object and its \(3\) times magnified virtual image as produced by a convex lens is \(20 \mathrm{~cm}\). The focal length of the lens used is _______ \(\mathrm{cm}\).

A uniform metallic wire carries a current \(2\,A\). when \(3.4\,V\) battery is connected across it. The mass of uniform metallic wire is \(8.92 \times 10^{-3} \,kg\). density is \(8.92 \times 10^3\,kg / m ^3\) and resistivity is \(1.7 \times 10^{-8} \Omega- m\). The length of wire is \(l=............\,m\)

A solid ball of radius \(R\) has a charge density \(\rho \) given by \(\rho  = {\rho _0}\left( {1 - \frac{r}{R}} \right)\) for \(0 \leq r \leq R\). The electric field outside the ball is

Radius of a certain orbit of hydrogen atom is \(8.48\mathring A \). If energy of electron in this orbit is \(\mathrm{E} / \mathrm{x}\), then \(\mathrm{x}=\) _______. (Given \(a_0=0.529 \mathring A, E=\) energy of electron in ground state)