Is it correct to say that C.M. of a system of n-particles is always given by the average position vectors of the consituent particles? If not, when is this statement true?

Two particles of equal masses m and m are connected by a light string of length 2l. A constant force F is applied continuously at the mid-point of the string, always along the perpendicular bisector of the straight line joining the two particles. Show that when the distance between the two particles is x, the acceleration of the particle is a = F/m = (x)/((1^2 - x^2) ^(1//2)

Read each statement below carefully and state with reasons, if it is true or false: the average speed of a particle is either greater than or equal to the magnitude of average velocity of the particle over the same interval of time.

The motion of a particle of mass m is given by x = 0 for t 0), and x = 0 for t > (1/4) s. which of the following statements is true?/

Read each statement below carefully and state with reasons, if it is true or false :- the average speed of a particle (defined as total path length divided by the time taken to cover the path) is either greater or equal to the magnitude of average velocity of the particle over the same interval of time,

Read each statement below carefully and state, with reasons, if it is true or false :- The velocity vector of a particle at a point is always along the tangent to the path of the particle at that point

If an a.c. main supply is given to be 220V, the average e.m.f. during a positive half cycle will be

A particle is in linear simple harmonic motion between two points, A and B, 10 cm apart. Take the direction from A to B as the positive direction and give the signs of velocity, acceleration and force on the particle when it is at the mid-point of AB going towards A,

Among the following which is/are correct statement about the metal sulphide sols ? the sol particles are positively charged due to preferential adsorption of metal ions, the sol particles are negatively charged due to preferential adsorption of sulphide ions, the cations of added electrolytes are effective in causing the coagulation of the sol, the sol is due to both the electric charge and hydration of the particles.

In these question, a statement of asertion followed by a statement of reason is given .Choose the correct answer out of the following choices: Assertion and reason both are correct statements and reason is correct explanation for assertion. Assertion and reason both are correct statements but reason is not correct explanation for assertion. Assertion is correct statement but reason is wrong statement. Assertion is wrong statement but reason is correct statement. Assertion:In high latitudes,one sees colourful curtains of ligth hanging down from high altitudes. Reason:The high enregy charged particles from the sun are deflected to polar regions by the magnetic field of the earth.

Three particles each of mass m are placed at the corners of a right angled triangle as shown in figure if OA=a and OB=b, the position vector of the centre of mass is: .