If one of the particle is heavier than the other, to which side will their centre of mass shift?

Eighteen guests have to be Seated, half on each side of a long table. Four particular guests desire to sit on one particular side and three others on the other side. Determine the number of ways in which the Seating arrangements can be made.

The extremities of the base of an isosceles triangle are the points (2a, 0) and (0, a). The equation of one of the sides is x = 2a. Find the equations of the other two sides and the area of the triangle.

Separation of mmotion of a systme of particles into motion of the centre of mass and motion about the centre of mass Show vecp = vec p_i + m_i vecV where vecp_i is the momentum of the ith particle

Separation of mmotion of a systme of particles into motion of the centre of mass and motion about the centre of mass Show K = K + 1/2 MV^2 , where k is the total kinetic energy of the system of particles, K is the total kinetic energy of the system when the particle velcoities are taken with respect to the centre of mass and MV^2//2 is the kinetic energy of the translation of the system as a whole (i,e of the centre of mass motion of the system).

Separation of mmotion of a systme of particles into motion of the centre of mass and motion about the centre of mass Show vec L = L = vec L + vecM R xx vecV where vec L = Sigma vecr_i xx vecp_i is the angular momentum of the system about the centre of mass with velocities taken relative to the centre of mass. Remember vecr_i = vecr_i - vecR , rest f the notation is the standard notation used in the chapter. Note vecL and vecMR xx vecV can be said to be angular moemnta respectively about and of the centre of mass of the system of particles.

Separation of Motion of a system of particles into motion of the centre of mass and motion about the centre of mass :- Show (dL')/(dt)=(sumr_i') xx (dp')/(dt) Further, show that (dL')/(dt)= tau'_(ext) where tau'_(ext) is the sum of all external torques acting on the system about the centre of mass.

One side of a rectangular piece of paper is 6 cm, the adjacent sides being longer than 6 cms. One corner of the paper is folded so that it sets on the opposite longer side. If the length of the crease is l cms and it makes an angle theta with the long side as shown, then l is

You have a bag of cotton and an iron bar, each indicating a mass of 100 kg when measured on a weighing machine. In reality, one is heavier than other. Can you say which one is heavier and why ?