A uniform cylindrical rod of length L and radius r, is made from a material whose Young’s modulus of Elasticity equals Y. When this rod is heated by temperature T and simultaneously subjected to a net longitudinal compressional force F, its length remains unchanged. The coefficient of volume expansion, of the material of the rod, is (nearly) equal to :

Find the magnetic field at point P due to a straight line segment AB of length 6 cm carrying a current of 5A. (See figure) ($$\mu $$₀ = 4$$\pi $$ × 10^–7 N-A^–2)

A spring whose unstretched length is l has a force constant k. The spring is cut into two pieces of unstretched lengths l₁ and l₂ where, l₁ = nl₂ and n is an integer. The ratio k₁/k₂ of the corresponding force constant, k₁ and k₂ will be :

The ratio of the weights of a body on the Earth’s surface to that on the surface of a planets is 9 : 4. The mass of the planet is $${1 \over 9}$$ th of that of the Earth. If 'R' is the radius of the Earth, what is the radius of the planet ? (Take the planets to have the same mass density)