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)

Moment of inertia of an equilateral triangular lamina ABC, about the axis passing through its centre O and perpendicular to its plane is I_o as shown in the figure. A cavity DEF is cut out from the lamina, where D, E, F are the mid points of the sides. Moment of inertia of the remaining part of lamina about the same axis is :

A 1 kg block attached to a spring vibrates with a frequency of 1 Hz on a frictionless horizontal table. Two springs identical to the original spring are attached in parallel to an 8 kg block placed on the same table. So, the frequency of vibration of the 8 kg block is :