A film of soap solution is formed between two straight parallel wires of length $$10 \mathrm{~cm}$$ each separated by $$0.5 \mathrm{~cm}$$. If their separation is increased by $$1 \mathrm{~mm}$$ while still maintaining their parallelism. How much work will have to be done?

(surface tension of solution $$=65 \times 10^{-2} \mathrm{~N} / \mathrm{m}$$ )

An ideal gas in a container of volume 500 c.c. is at a pressure of $$2 \times 10^{+5} \mathrm{~N} / \mathrm{m}^2$$. The average kinetic energy of each molecule is $$6 \times 10^{-21} \mathrm{~J}$$. The number of gas molecules in the container is

A gas at N.T.P. is suddenly compressed to onefourth of its original volume. If $$\gamma=1.5$$, then the final pressure is

A particle of mass '$$\mathrm{m}$$' moves along a circle of radius '$$r$$' with constant tangential acceleration. If K.E. of the particle is '$$E$$' by the end of third revolution after beginning of the motion, then magnitude of tangential acceleration is