A small ball of mass m is thrown upward with velocity u from the ground. The ball experiences a resistive force mkv² where v is its speed. The maximum height attained by the ball is :

A quantity x is given by $$\left( {{{IF{v^2}} \over {W{L^4}}}} \right)$$ in terms of moment of inertia I, force F, velocity v, work W and Length L. The dimensional formula for x is same as that of :

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 :

A paramagnetic sample shows a net magnetisation of 6 A/m when it is placed in an external magnetic field of 0.4 T at a temperature of 4 K. When the sample is placed in an external magnetic field of 0.3 T at a temperature of 24 K, then the magnetisation will be: