A particle of charge q and mass m is subjected to an electric field
E = E₀ (1 – $$a$$x²) in the x-direction, where $$a$$ and E₀ are constants. Initially the particle was at rest at x = 0. Other than the initial position the kinetic energy of the particle becomes zero when the distance of the particle from the origin is :

Find the Binding energy per neucleon for $${}_{50}^{120}Sn$$. Mass of proton m_p = 1.00783 U, mass of neutron m_n = 1.00867 U and mass of tin nucleus m_Sn = 119.902199 U. (take 1U = 931 MeV)

A capacitor C is fully charged with voltage V₀. After disconnecting the voltage source, it is connected in parallel with another uncharged capacitor of capacitance $${C \over 2}$$. The energy loss in the process after the charge is distributed between the two capacitors is :

A body is moving in a low circular orbit about a planet of mass M and radius R. The radius of the orbit can be taken to be R itself. Then the ratio of the speed of this body in the orbit to the escape velocity from the planet is: