The work done in displacing a particle from $y=a$ to $y=2 a$ by a force $-\frac{K}{y^2}$ acting along $Y$-axis is

Due to the presence of air resistance, if a body dropped from a height of 20 m reaches the ground with a speed of $18 \mathrm{~ms}^{-1}$, then the time taken by the body to reach the ground is nearly

A balance is made using a uniform metre scale of mass 100 g and two plates each of mass 200 g fixed at the two ends of the scale and the balance is pivoted at 45 cm mark of the scale. The error when 300 g weight is placed in the plate at 0 cm to weigh vegetables placed in the plate at 100 cm is

The ratio of radii of gyration of a thin circular ring and a circular disc of same radius about a tangential axis in their own planes is $\sqrt{12}: \sqrt{K}$. The value of $K$ is