A magnetic needle suspended parallel to a magnetic field requires $$\sqrt 3 J$$ of work to turn it through 60^o. The torque needed to maintain the needle in this position will be

A cell having an emf $$\varepsilon $$ and internal resistance r is connected across a variable external resistance R. As the resistance R is increased, the plot of potential difference V across R is given by

An ideal gas goes from state A to state B via three different processes as indicated in the P-V diagram.



If Q₁, Q₂, Q₃ indicate the heat absorbed by the gas along the three processes and $$\Delta $$U₁, $$\Delta $$U₂, $$\Delta $$U₃ indicate the change in internal energy along the three processes respectively, then

The equation of a simple harmonic wave is given by

y = 3 sin$${\pi \over 2}$$(50t $$-$$ x),

where x and y are in metres and t is in seconds. The ratio of maximum particle velocity to the wave velocity is