1. In Searle’s apparatus diameter of the wire was measured 0.05 cm by screw gauge of least count 0.001 cm.The length of wire was measured 110 cm by meter scale of least count 0.1 cm. An external load of 50 N was applied. The extension in length of wire was measured 0.125 cm by micrometer of least count 0.001 cm. Find the maximum possible error in measurement of young’s modulus.
2. Two infinitely large sheets having charge densities σ1 and σ2
respectively (σ1 > σ2) are placed near each other separated by
distance ‘d’. A charge ‘Q’ is placed in between two plates such that
there is no effect on charge distribution on plates. Now this charge
is moved at an angle of 45° with the horizontal towards plate having
charge density σ2 by distance ‘a’ (a is l.t. d). Find the work done by
electric field in the process.
3. An α -particle and a proton are accelerated from rest through same potential difference and both enter into a uniform perpendicular magnetic field. Find the ratio of their radii of curvature.
4. A small ball of radius ‘r’ is falling in a viscous liquid under gravity. Find the dependency of rate of heat produced in terms of radius ‘r’ after the drop attains terminal velocity.
5. A screw gauge of pitch 1mm has a circular scale divided into 100 divisions. The diameter of a wire is to be measured by above said screw gauge. The main scale reading is 1mm and 47th circular division coincides with main scale. Find the curved surface area of wire in true significant figures. (Given the length of wire
is equal to 5.6 cm and there is no zero-error in the screw gauge.)
Source: 2004 JEE mains