A wooden log of mass M and length L is hinged by a frictionless nail at O; a bullet of mass m strikes with velocity $$v$$ and sticks to it. Find angular velocity of the system immediately after the collision about O.

What will be the minimum angle of incidence such that the total internal reflection occurs on both the surfaces?

The side of a cube is measured by vernier callipers (10 divisions of a vernier scale coincide with 9 divisions of main scale, where 1 division of main scale is 1 mm). The main scale reads 10 mm and first division of vernier scale coincides with the main scale; Mass of the cube is 2.736 g. Find the density of the cube in appropriate significant figures.

An unknown resistance X is to be determined using resistances R$$_1$$, R$$_2$$ or R$$_3$$. Their corresponding null points are A, B and C. Find which of the above will give the most accurate reading and why ?