Classical Mechanics Answers

If m_1,m₂ and m₃ be the masses of three particles v_12, v₂₃ and v₁₃ be their relative velocities, prove that the total kinetic energy (E) of the system about the centre of mass is given by

m₁m₂v²₁₂₊ m₂m₃v²₂₃₊ m₁m₃v²₁₃ / m₁+ m₂ + m₃

Radius of capillary is 2mm. A liquid of weight 6.28 x 10^-4N may remain in the capillary, then the surface tension of liquid will be?

A ball moving along the x -axis bounces elastically off a horizonal wall that runs in along y-axis. The magnitude of the momentum of the ball is the same before and after the collision. Explain how we can conclude that the ball-wall system is closed but not isolated. 

*Conservative force and its potential energy function Consider the components of a position dependent force F(r): Fx = ayz + bx + c Fy = axz + bz Fz = axy + by. (a) Show that this force is conservative. (b) Find its corresponding potential energy function, V (r)

In an experiment using a linear air track a 0.5kg rider travelling to the right at 2m/s collides with a stationary rider of mass 1kg find the velocities of the two riders after collision if it is perfectly elastic

2.3 The width of a confidence interval is a measure of its precision. The narrower the confidence interval, the more precise is the interval estimate, and vice versa. Describe any three aspects that influence the precision of the width of a confidence interval of a single population mean.