Answer:

Explanation:
Mass: M, Length: L.

The formula that gives center of mass is

In the case of a non-uniform mass density, this formula converts to

where the denominator is the total mass and the nominator is the mass times position of each point on the rod.
We have to integrate the mass density over the total rod in order to find the total mass. Likewise, we have to integrate the center of mass of each point (xσ(x)) over the total rod. And if we divide the integrated center of mass to the total mass, we find the center of mass of the rod:

Here x's are cancelled. Otherwise, the denominator would be zero.

Answer:
C) Use a battery with more voltage.
Explanation:
The equation for the magnetic field around a coil is given by,
B = μ₀NI
where,
B = Magnetic flux density
μ₀ = permeability
N = number of turns per meter
I = Current in the wire
So when using a higher voltage battery, more current passes through the battery as resistance of the wire remains the same.
Explanation:
Given that,
Potential difference, V = 412 V
Magnitude of magnetic field, B = 188 mT
(a) The potential energy of electron is balanced by its kinetic energy as :

v is speed of the electron

(b) When the charged particle moves in magnetic field, it will move in circular path. The radius of the circular path is given by :

Hence, this is the required solution.
Answer:
D
Explanation:
I am assuming that you got to go up to Zak as his editor and tell him in his face if he is doing the work correctly. Dont trust me though, cause C also looks plausible
Efficiency of a simple machine is the ratio of mechanical advantage and speed ratio.
If mechanical advantage = speed ratio then efficiency = 1
Which is impossible for a practical machine due to presence of frictional force which wastes some energy and thus lowers the output