A force $$\mathbf{F}=-k(y \hat{\mathbf{i}}+x \hat{\mathbf{j}})$$ where $$k$$ is a positive constant, acts on a particle moving in the $$x y$$ plane. Starting from the origin, the particle is taken along the positive $$x$$-axis to the point $$(a, 0)$$ and then parallel to the $$y$$-axis to the point $$(a, a)$$. The total work done by the force on the particle is

A block is dragged on a smooth plane with the help of a rope which moves with a velocity v as shown in the figure. The horizontal velocity of

A person of weight $$70 \mathrm{~kg}$$ wants to loose $$7 \mathrm{~kg}$$ by going up and down $$12 \mathrm{~m}$$ high stairs. Assume he burns twice as much fat while going up than going down. If $$1 \mathrm{~kg}$$ of fat is burnt on expending 9000 k-cal. How many times must he go up and down to reduce his $$7 \mathrm{~kg}$$ weight?

(Take $$g=10 \mathrm{~ms}^{-2}$$)