Two moles of helium gas are taken over the cycle $$ABCD$$, as shown in the $$P$$-$$T$$ diagram.

The net work done on the gas in the cycle $$ABCDA$$ is:

Two wires are made of the same material and have the same volume. However wire $$1$$ has cross-sectional area $$A$$ and wire $$2$$ has cross-sectional area $$3A.$$ If the length of wire $$1$$ increases by $$\Delta x$$ on applying force $$F,$$ how much force is needed to stretch wire $$2$$ by the same amount?

A thin uniform rod of length $$l$$ and mass $$m$$ is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is $$\omega $$. Its center of mass rises to a maximum height of:

The height at which the acceleration due to gravity becomes $${g \over 9}$$ (where $$g=$$ the acceleration due to gravity on the surface of the earth) in terms of $$R,$$ the radius of the earth, is: