Physics

In the hydrogen spectrum, $\lambda$ be the wavelength of first transition line of Lyman series. The wavelength difference will be $"a\lambda "$ between the wavelength of 3rd transition line of Paschen series and that 2nd transition line B Balmer series where a = __________.

The graph between $\frac{1}{u}and\frac{1}{v}$ for a thin convex lens in order to determine its focal length is plotted as shown in the figure. The refractive index of lens is 1.5 and its both the surfaces have same radius of curvature R. The value of R will be _________cm. (where u = object distance, v = image distance)

The effective current I in the given circuit at very high frequencies will be _________A.

In the given figure, the face AC of the equilateral prism is immersed in a liquid of refractive index 'n'. For incident angle $60°$ at the side AC, the refracteel light beam just grazes along face AC. The refractive index of the liquid $n=\frac{\sqrt[]{x}}{4}.$

The value of x is_______.

(Given refractive index of glass = 1.5)

The radius of gyration of a cylindrical rod about an axis of rotation perpendicular to its length and passing through the centre will be________m.

Given, the length of the rod is $10\sqrt[]{3}m.$

Resistances are connected in a meter bridge circuit as shown in the figure. The balancing length ${\mathcal{l}}_2$ is 40cm. Now as unknown resistance x is connected in series with P and new balancing length is found to be 80cm measured from the same end. Then the value of x will be _________ $\mathrm{\Omega .}$

If $\overline{A}=\left(2\widehat{i}+3\widehat{j}-\widehat{k}\right)mand\overrightarrow{B}=\left(\widehat{i}+2\widehat{j}+2\widehat{k}\right)m.$ The magnitude of component of vector $\overrightarrow{A}$ along vector $\overrightarrow{B}$ will be________m.

A composite parallel plate capacitor is made up to two different dielectric materials with different thickness (t₁ and t₂) as shown in figure. The two different dielectric materials are separated by a conducting foil F. The  voltage of the conducing foil is ___________V.

The area of cross section of the rope used to lift a load by a crane is 2.5 * 10^-4m². The maximum lifting capacity of the crane is 10 metric tons. To increase the lifting capacity of the crane to 25 metric tons, the required area of cross section of the rope should be:

When a car is approaching the observer, the frequency of horn is 100Hz. After passing the observer, it is 50 Hz. If the observer moves with the car, the frequency will be $\frac{x}{3}$ Ha where x = _________.