An ideal gas of mass $$m$$ in a state $$A$$ goes to another state $$B$$ via three different processes as shown in figure. If $$Q_1, Q_2$$ and $$Q_3$$ denote the heat absorbed by the gas along the three paths, then
A metal wire has a resistance of $$35 \Omega$$. If its length is increased to double by drawing it, then its new resistance will be
A half ring of radius $$R$$ has a charge of $$\lambda$$ per unit length. The electric force on $$1 \mathrm{C}$$ charged placed at the centre is
Positive charge $$Q$$ is distributed uniformly over a circular ring of radius $$R$$. A point particle having a mass $$(m)$$ and a negative charge $$-q$$ is placed on its axis at a distance $$x$$ from the centre. Assuming $$x < R$$, find the time period of oscillation of the particle, if it is released from there [neglect gravity].