A copper wire is stretched to make it 0.5% longer. The percentage change in its electrical resistance if its volume remains unchanged is :

Consider a tank made of glass(refractive index 1.5) with a thick bottom. It is filled with a liquid of refractive index $$\mu $$. A student finds that, irrespective of what the incident angle i (see figure) is for a beam of light entering the liquid, the light reflected from the liquid glass interface is never completely polarized. For this to happen, the minimum value of $$\mu $$ is :

A heavy ball of mass M is suspendeed from the ceiling of a car by a light string of mass m (m < < M). When the car is at rest, the speed of transverse waves in the string is 60 ms^$$-$$1. When the car has acceleration a, the wave-speed increases to 60.5 ms^$$-$$1. The value of a, in terms of gravitational acceleration g, is closest to :

For a uniformly charged ring of radius R, the electric field on its axis has the largest magnitude at a distance h from its center. Then value of h is :