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

A body of mass 500 g is falling from rest from a height of 3.2 m from the ground. If the body reaches the ground with a velocity of $6 \mathrm{~ms}^{-1}$, then the energy lost by the body due to air resistance is (Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

A constant force of $(8 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}+6 \hat{\mathbf{k}}) \mathrm{N}$ acting on a body of mass 2 kg displaces the body from $(2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}-4 \hat{\mathbf{k}}) \mathrm{m}$ to $(4 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+6 \hat{\mathbf{k}}) \mathrm{m}$. The work done in the process is

The kinetic energy of a body of mass 4 kg moving with a velocity of $(2 \hat{\mathbf{i}}-4 \hat{\mathbf{j}}-\hat{\mathbf{k}}) \mathrm{ms}^{-1}$ is