Astraight rod has one end at the origin and the other end at the point (l,0) and a linear density given by λ=ax2, where a is a known constant and x is the x coordinate. since this wire is not uniform, you will have to use integrtation to solve this part. use m=∫l0dm to find the total mass m. find xcm for this rod. express your answer in terms of one or both of a and l.

It is given that a straight rod has one end at the origin (that is (0,0)) and the other end at the point (L,0) and a linear density given  by, where a is a known constant and x is the x coordinate.

Therefore, the infinitesimal mass is given as:

Therefore, the total mass will be the integration of the above equation as:

Therefore,

Now, we can find the center of mass, of the rod as:

Now, we have

x_{cm}=\frac{1}{\frac{aL^3}{3}}\int_{0}^{L}ax^3dx=\frac{3}{aL^3}\times [\frac{ax^4}{4}]_{0}^{L}

Therefore, the center of mass, is at:

x+y=90

x=30-y=x

step-by-step explanation:

if you understand you will get the answer

answer:

the position of equilibrium will shift to the left.

step-by-step explanation:

the general equation for the dissociation of a weak base is

b + h₂o   ⇌   bh⁺ + oh⁻

according to le châtelier's principle, when a stress is applied to a system at equilibrium, the system will respond in a way that tends to relieve the stress.

if you apply a stress by adding more bh⁺ or oh⁻,   the system will respond by moving in a direction that gets rid of the added ions.

the position of equilibrium will shift to the left, forming more of the undissociated base.