The radii of two planets are respectively $R_1$ and $R_2$ and their densities are respectively $\rho_1$ and $\rho_2$. The ratio of the accelerations due to gravity at their surfaces is

The following observations were taken for determining the surface tension $T$ of water by the capillary method:
Diameter of capillary,$D = 1.25 \times 10^{-2} \ m$
Rise of water,$h = 1.45 \times 10^{-2} \ m$
Using $g = 9.80 \ m/s^2$ and the simplified relation $T = \frac{rhg}{2} \times 10^3 \ N/m$,the possible error in surface tension is closest to ......... $\%$

$A$ tangent galvanometer has a coil of $25$ turns and a radius of $15 \, cm$. The horizontal component of the earth's magnetic field is $3 \times 10^{-5} \, T$. The current required to produce a deflection of $45^o$ in it is.....$A$

$5.6 \ L$ of helium gas at $STP$ is adiabatically compressed to $0.7 \ L$. Taking the initial temperature to be $T_1$,the work done in the process is

If $f(x) = x^5 - 5x^4 + 5x^3 - 10$ has local maximum and minimum at $x = p$ and $x = q$,respectively,then $(p, q)$ equals

The resolving limit of a healthy human eye is about