The orbit of the earth is an ellipse wite eccentricity 0.0167. Determine the ratio of the maximum speed of the earth to its minimum speed.

A solid sphere of mass 6\text{ kg}, diameter 20\text{ cm}, and uniform density rolls over a surface with a speed of 2\text{ ms}^{-1}. Calculate its kinetic energy.

Write a note on Bernoulli's theorem and its applications.

A rocket is fired vertically up. During the burning of the engine, which lasts for 50\text{ s}, a constant acceleration of 2.0\text{ g} is observed. What is the speed of the rocket at the end of 50\text{ s}? Calculate the maximum height to which the rocket will rise before it begins to fall back. Take = g = 9.80\text{ ms}^{-2} and neglect the variation of g with height.

Water is observed to flow through a capillary of diameter 1.0\text{ mm} with a speed of 3\text{ ms}^{-1} viscosity of water in c.g.s. units is : 0.018 at 0^{\circ}\text{C} 0.008 at 30^{\circ}\text{C} 0.004 at 70^{\circ}\text{C} Calculate he Reynolds numbers, and test at which of these three temperatures is the flow likely to be streamlined.

Explain clearly why Young's modules Y of a material determines the resistance to bending of a thin rod made of that material. Derive the expression for the work done when a wire of length l and cross-sectional area A is stretched by an amount x(\le l) under a given load corresponding to equilibrium at stretching x.

A neutron having kinetic energy E collides head on with a _{6}^{12}\text{C} nucleus and rebounds perfectly elastically in the direction from which it came. Determine the kinetic energy of the neutron after collision.

Calculate the velocity of an electron having kinetic energy 1 MeV.

The earth receives from the Sun 1.37\times 10^{3}\text{ W/m}^{2} of power on the top of the atmosphere. Calculate the mass of the Sun that is converted into energy in one second.