A) Find the xcm coordinate of the center of mass of the system of particles shown in the figure. (See attached file for full problem description with diagram and values)

Express your answer in meters to two significant figures.
xcm =

B) A straight rod has one end at the origin and the other end at the point (L,0) and a linear density given by lambda = ax^2 , where is a known constant and is the x coordinate. Since this wire is not uniform, you will have to use integration to solve this part. Use this integration formula to find the total mass . Find xcm for this rod.
Express your answer in terms of one or both of a and L .
xcm =

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Solution Summary

This solution contains step-by-step explanations and calculations to determine the xcm coordinate of the center of mass for the system of particles and for the rod. All workings and formulas are shown for further understanding.

... For the system of particles described above, find the x coordinate of the center of mass. Assume that the particle of mass M is at the origin and the positive ...

... And hence the position of the particle of mass m1 as a function of time with initial position of center of mass as origin is given by = position of center of ...

... Since the rod is of length L we need only the X component of the centre of mass. We know that for a collection of particles, the CM is given by summing the ...

... and (c) lies in the plane of the square and passes through two diagonally opposite particles ? ... We calculate the energy by knowing the center of mass of the ...

... of the particle of mass m at the surface of the earth is. U0 = - GMm/R. And its potential energy in the hole when it is at the distance x from the center of ...

... Solution: Let the instantaneous position of the two particles be x1 and x2 respectively. 0 x1 x2 m1=2kg m2=1kg. Centre of mass of the two particle system = xc ...

... be described as a pure translational motion of its center of mass as a single particle, and a pure rotational motion of the particles about the center of mass. ...

A particle of mass m is constrained to move on a ... of a gravitational force, show that the particle's motion about ... through the pivot point and the center of the ...

... you say about the motion of the particles in the centre of momentum ... annihilates the two photons and produces two new particles of equal rest mass m. Show ...