A rod, of length L at room temperature and uniform area of cross section A, is made of a metal having coefficient of linear expansion $$\alpha $$/^oC. It is observed that an external compressive force F, is applied on each of its ends, prevents any change in the length of the rod, when its temperature rises by $$\Delta $$TK. Young's modulus, Y, for this metal is :

A gas can be taken from A to B via two different processes ACB and ADB.


When path ACB is used 60 J of heat flows into the system and 30 J of work is done by the system. If path ADB is used work done by the system is 10 J. The heat Flow into the system in path ADB is :

A plane electromagnetic wave of frequency 50 MHz travels in free space along the positive x-direction. At a particular point in space and time, $$\overrightarrow E = 6.3\widehat j\,V/m.$$ The corresponding magnetic field $$\overrightarrow {B,} $$ at that point will be :

A particle is moving with a velocity

$$\overrightarrow v \, = K(y\widehat i + x\widehat j),$$ where K is a constant.

The general equation for its path is :