The displacement x of a particle at time t moving under a constant force is t = $\sqrt{\mathrm{x}}$ + 3, x in metre, t in second. Find the work done by the interval from t = 0 to t= 6 s.

Calculate the distance below and above the surface of the earth, at which the value of acceleration due to gravity becomes 1/4th that at earth's surface ?

Two cells each of same emf e but of internal resistances r₁ and r₂ are connected in series through an external resistance R. If the potential difference between the ends of the first cell is zero, what will be the value of R in terms of r₁ and r₂ ?

A ray of light travelling inside a rectangular glass block of refractive index $\sqrt{2}$ is incident on the glass-air surface at an angle of incidence of 45°. Show that the ray will emerge into the air at an angle of refraction equal to 90°.

45.

At time t = O, a radioactive sample has a mass of 10 g. Calculate the expected mass of radioactive sample after two successive mean lives.