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All the particles of a body are situate at a distance R from the origin. The distance of the centre of mass of the body from the origin is

(a) = R (b) <=R (c) >R (d) >=R

d(log|x|)/dx

Case I. If x >0; |x| = x;

So d(logx)/dx = 1/x.

Case II. If x <0; |x| = -x;

So d(log(-x))/dx = 1/(-x) * d(-x)/dx

= 1/x;

So Ans is 1/x.

A small particle travelling with a velocity v collides elastically with a spherical body of equal mass and of radius r initially kept at rest. The centre of the spherical body is located at a distance p(<r) away from the direction of motion of the particle.Find the final velocities of the two particles. ( This is from HC Verma Centre of mass, collision... Prob.64 )

A uniform chain of mass M and length L is held vertically in such a way that its lower end just touches the horizontal floor. The chain is released from rest in this position. Any portion that strikes the ground comes to rest. Assuming that the chain does not form heap on the floor, calculate the force exerted by it on the floor when a length x has reached the floor...