A cubical region of side $$a$$ has its center at the origin. It encloses three fixed point charges, $$-q$$ at $$\left( {0, - a/4,0} \right), + 3q$$ at $$\left( {0,0,0} \right)$$ and $$-q$$ at $$\left( {0, + a/4,0} \right).$$ Choose the correct option(s)

Consider a thin spherical shell of radius $$R$$ with center at the origin, carrying uniform positive surface charge density. The variation of the magnitude of the electric field $$\left| {\overrightarrow E \left( r \right)} \right|$$ and the electric potential $$V(r)$$ with the distance $$r$$ from the center, best represented by which graph?

A mixture of 2 moles of helium gas (atomic mass = 4 amu) and 1 mole of argon gas (atomic mass = 40 amu) is kept at 300 K in a container. The ratio of the rms speeds $$\left( {{{{v_{rms}}\left( {helium} \right)} \over {{v_{rms}}\left( {\arg on} \right)}}} \right)$$ is

In the determination of Young's modulus $$\left( {Y = {{4MLg} \over {\pi l{d^2}}}} \right)$$ by using Searle's method, a wire of length L = 2 m and diameter d = 0.5 mm is used. For a load M = 2.5 kg, an extension l = 0.25 mm in the length of the wire is observed. Quantities d and l are measured using a screw gauge and a micrometer, respectively. They have the same pitch of 0.5 mm. The number of divisions on their circular scale is 100. The contributions to the maximum probable error of the Y measurement