A bottle has an opening of radius a and length b. A cork of length b and radius (a + $$\Delta $$a) where ($$\Delta $$a < < a) is compressed to fit into the opening completely (See figure). If the bulk modulus of cork is B and frictional coefficient between the bottle and cork is $$\mu $$ then the force needed to push the cork into the bottle is :

In the figure shown ABC is a uniform wire. If centre of mass of wire lies vertically below point A, then $${{BC} \over {AB}}$$ is close to :

Velocity-time graph for a body of mass 10 kg is shown in figure. Work-done on the body in first two seconds of the motion is :

To determine refractive index of glass slab using a travelling microscope, minimum number of readings required are :