The magnetic field B crossing normally a square metallic plate of area $$4 \mathrm{~m}^{2}$$ is changing with time as shown in figure. The magnitude of induced emf in the plate during $$\mathrm{t}=2 s$$ to $$\mathrm{t}=4 s$$, is __________ $$\mathrm{mV}$$.

A force $$\vec{F}=(2+3 x) \hat{i}$$ acts on a particle in the $$x$$ direction where F is in newton and $$x$$ is in meter. The work done by this force during a displacement from $$x=0$$ to $$x=4 \mathrm{~m}$$, is __________ J.

A solid sphere of mass $$500 \mathrm{~g}$$ and radius $$5 \mathrm{~cm}$$ is rotated about one of its diameter with angular speed of $$10 ~\mathrm{rad} ~\mathrm{s}^{-1}$$. If the moment of inertia of the sphere about its tangent is $$x \times 10^{-2}$$ times its angular momentum about the diameter. Then the value of $$x$$ will be ___________.

The length of a wire becomes $$l_{1}$$ and $$l_{2}$$ when $$100 \mathrm{~N}$$ and $$120 \mathrm{~N}$$ tensions are applied respectively. If $$10 ~l_{2}=11~ l_{1}$$, the natural length of wire will be $$\frac{1}{x} ~l_{1}$$. Here the value of $$x$$ is _____________.