The ratio of maximum acceleration to maximum velocity in a simple harmonic motion is 10 s⁻¹ . At, t = 0 the displacement is 5 m. What is the maximum acceleration ? The initial phase is $${\pi \over 4}$$.

A compressive force, F is applied at the two ends of a long thin steel rod. It is heated, simultaneously, such that its temperature increases by $$\Delta $$T. The net change in its length is zero. Let $$\ell $$ be the length of the rod, A its area of cross-section,Y its Young’s modulus, and $$\alpha $$ its coefficient of linear expansion. Then, F is equal to :

An object is dropped from a height h from the ground. Every time it hits the ground it looses 50% of its kinetic energy. The total distance covered as t $$ \to $$ $$\infty $$ is :

In an experiment, a sphere of aluminium of mass 0.20 kg is heated upto 150^oC. Immediately, it is put into water of volume 150 cc at 27^oC kept in a calorimeter of water equivalent to 0.025 kg. Final temperature of the system is 40^oC. The specific heat of aluminium is : (take 4.2 Joule = 1 calorie)