A person pushes a box on a rough horizontal platform surface. He applies a force of 200 $\mathrm{N}$ over a distance of $15\mathrm{m}$ . Thereafter, he gets progressively tired and his applied force reduces linearly with distance to $100\mathrm{N}$ . The total distance through which the box has been moved is $30\mathrm{m}$ . What is the work done by the person during the total movement of the box?

Particle $A$ of mass $m_A=\frac{m}{2}$ moving along the $x$ -axis with velocity $v_0$ collides elastically with another particle $B$ at rest having mass $m_B=\frac{m}{3}$ . If both particles move along the $x$ axis after the collision, the change $\mathrm{\Delta }\lambda$ in de-Broglie wavelength of particle $A$ , in terms of its de-Broglie wavelength $\left({\lambda }_0\right)$ before collision is:

A wire $A$ , bent in the shape of an arc of a circle, carrying a current of $2\mathrm{A}$ and having radius $2\mathrm{c}\mathrm{m}$ and another wire $B$ , also bent in the shape of arc of a circle, carrying a current of $3\mathrm{A}$ and having radius of $4\mathrm{c}\mathrm{m}$ , are placed as shown in the figure. The ratio of the magnetic fields due to the wires $A$ and $B$ at the common centre $O$ is: