Consider a Disc of mass $$5 \mathrm{~kg}$$, radius $$2 \mathrm{~m}$$, rotating with angular velocity of $$10 \mathrm{~rad} / \mathrm{s}$$ about an axis perpendicular to the plane of rotation. An identical disc is kept gently over the rotating disc along the same axis. The energy dissipated so that both the discs continue to rotate together without slipping is ________ J.

The displacement and the increase in the velocity of a moving particle in the time interval of $$t$$ to $$(t+1) \mathrm{s}$$ are $$125 \mathrm{~m}$$ and $$50 \mathrm{~m} / \mathrm{s}$$, respectively. The distance travelled by the particle in $$(\mathrm{t}+2)^{\mathrm{th}} \mathrm{s}$$ is _________ m.

Each of three blocks $$\mathrm{P}, \mathrm{Q}$$ and $$\mathrm{R}$$ shown in figure has a mass of $$3 \mathrm{~kg}$$. Each of the wires $$\mathrm{A}$$ and $$\mathrm{B}$$ has cross-sectional area $$0.005 \mathrm{~cm}^2$$ and Young's modulus $$2 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}$$. Neglecting friction, the longitudinal strain on wire $$B$$ is ________ $$\times 10^{-4}$$. (Take $$\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$$)

A ceiling fan having 3 blades of length $$80 \mathrm{~cm}$$ each is rotating with an angular velocity of 1200 $$\mathrm{rpm}$$. The magnetic field of earth in that region is $$0.5 \mathrm{G}$$ and angle of dip is $$30^{\circ}$$. The emf induced across the blades is $$\mathrm{N} \pi \times 10^{-5} \mathrm{~V}$$. The value of $$\mathrm{N}$$ is _________.