The P.E. 'U' of a moving particle of mass 'm' varies with 'x'-axis as shown in figure. The deBroglie wavelength or the particle in the regions $$0 \leq x \leq 1$$ and $$x > 1$$ are $$\lambda_1$$ and $$\lambda_2$$ respectively. II the total energy of the particle is '$$\mathrm{nE}$$', then the ratio $$\lambda_1 / \lambda_2$$ is
An inductive coil has a resistance of $$100 ~\Omega$$. When an a.c. signal of frequency $$1000 \mathrm{~Hz}$$ is applied to the coil the voltage leads the current by $$45^{\circ}$$. The inductance of the coil is $$\left(\tan 45^{\circ}=1\right.$$)
The ratio of radii of gyration of a circular ring and circular disc of the same mass and radius, about an axis passing through their centres and perpendicular to their planes is
Two wires carrying currents $$5 \mathrm{~A}$$ and $$2 \mathrm{~A}$$ are enclosed in a circular loop as shown in the figure. Another wire carrying a current of $$3 \mathrm{~A}$$ is situated outside the loop. The value of $$\oint \overrightarrow{\mathrm{B}} \overrightarrow{\mathrm{d} l}$$ around the loop is ( $$\mu_0=$$ permeability of free space, $$\overrightarrow{\mathrm{d} l}$$ is the length of the element on the Amperion loop)
