$A$ photon and an electron are given the same energy $(10^{-20} \ J)$. If the wavelengths associated with the photon and the electron are $\lambda_{ph}$ and $\lambda_{el}$ respectively,then which of the following statements is correct?

An artificial satellite of mass $m$ is moving along an elliptical path around the Earth. The areal velocity of the satellite is proportional to

The acceleration due to gravity is measured on the surface of the Earth by using a simple pendulum. If $\alpha$ and $\beta$ are relative errors in the measurement of length and time period respectively,then the percentage error in the measurement of acceleration due to gravity is ................

Two rods of different materials having coefficients of linear expansion $\alpha_1$ and $\alpha_2$ and Young's moduli $Y_1$ and $Y_2$ respectively are fixed between two rigid massive walls. The rods are heated such that they undergo the same increase in temperature. There is no bending of rods. If $\alpha_1 : \alpha_2 = 2 : 3$,the thermal stress developed in the two rods is equal provided $Y_1 : Y_2$ is equal to:

The differential equation of the family of parabolas with vertex at $(0, -1)$ and having axis along the $Y$-axis is

Wavelengths of light used in an optical instrument are $\lambda_1 = 4000 \ Å$ and $\lambda_2 = 5000 \ Å$. The ratio of their respective resolving powers (corresponding to $\lambda_1$ and $\lambda_2$) is: