The figure shows a mass $m$ on a frictionless surface. It is connected to rigid wall by the mean of a massless spring of its constant $k$. Initially, the spring is at its natural position. If a force of constant magnitude starts acting on the block towards right, then the speed of the block when the deformation in spring is $x$, will be

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