A nucleus with mass number $A =240$ and binding energy per nucleon $=7.6 MeV$ breaks into two fragments each of $A =120$ with binding energy per nucleon $= 8.5 MeV $. Calculate the released energy.
(a) For what Kinetic energy of a neutron, will the associated de-Broglie wavelength be $1.40 \times 10^{-10} m$ ? (b) Find the de-Broglie wavelength of a neutron, in thermal equilibrium with matter, having an average Kinetic energy of $\frac{3}{2} K_{ a } T$ at 300 K . $\left[ K _{ B }=1.38 \times 10^{-23}\right.$ SI unit $]$
A beam of light consisting of two wavelengths 6000 Å and 4000 Å, is used to obtain interference fringes in a Young's double-slit experiment. (a) Find the distance of the third dark fringe on the screen from the central maximum for wavelength 6000 Å . (b) What is the least distance from the central maximum where bright fringes due to both the wavelengths coincide? (Distance between two slits $=0.1 mm$. Take $D =100 cm$ )
(a) The radii of curvature of the faces of a double convex lens are 10 cm and 15 cm . Its focal length is 12 cm . What is the refractive index of glass? (b) A convex lens has 15 cm focal length in air. What is focal length in water? (Refractive index of air-water 1.33 and Refractive index of air-glass $=1.5$ )
A circular coil of radius 8 cm and 20 turns is rotated about its vertical diameter with an angular speed of $50 rad s ^{-1}$ in a uniform horizontal magnetic field of magnitude $3 \times 10^{-2} T$. Obtain the maximum and average emf induced in the coil. If the coil forms a closed loop of resistance $10 \Omega$, calculate the maximum value of current in the coil.
Two long and parallel straight wires $A$ and $B$ carrying currents of 8 A and 5 A in the same direction are separated by a distance of 4 cm . Estimate the force on a 10 cm section of wire A .
A heating element using nichrome connected to a 230 V supply draws an initial current of 4.6 A which settles after a few seconds to a steady value of 2.3 A . What is the steady temperature of the heating element if the room temperature is $27^{\circ} C$. [ $\left.\alpha=1.7 \times 10^{-4}{ }^{\circ} C ^{-1}\right]$