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How to determine the diameter of a rod using thread an meter scale?

You are given a sufficiently long piece of thread, a meter stick and a thin round shape iron rod. Explain how would you measure the diameter of iron rod by using given thread and meter stick.

Yosef asked

Answer:

thread wound on rodWind the thread over the rod  closely a number of times say 20 and mark the end point. Now unwind it and measure the length of the thread used to wind over the rod.

This length = n x 2πr, where n is the no. of windings and r is the radius of the rod.

Therefore, the diameter of the rod = 2r = The length of wire used for ‘n’ windings /nπ

How wheel + Tyre diameter affects a vehicle’s speed

I have been told a larger wheel/tyre decrease acceleration because its harder to turn the wheel making the car rev slower.

But the same person tells me it will increase the top speed.

My question is if the car has a max rev of 8000rpm but only reaches 7000rpm in its highest gear would a smaller wheel/tyre not make it easier for the car to rev higher thus possible increasing the top speed by using a smaller wheel?

(Garry asked)

Answer:
As wheel radius increases, its top speed increases for a given RPM since for a given RPM the speed of the vehicle is directly proportional to its radius.
The distance traveled in one rotation = 2 π R
But now, there is another effect also here. As the radius of tyre increases, its moment of inertia increases and it would be harder for the engine to rotate it. So, the engine will not be able to turn it with the same ease as before, but however, there will be an increase in top speed other conditions remaining the same.
Monster Truck
Refer to http://wahiduddin.net/calc/calc_speed_rpm.htm for a calculation of top speed vs tyre radius

Wire Gauge and Resistance problem

I am using 18 gauge nicrome wire having ohm of 17.3 , 220 volt. I want to use 10 gauge wire how to decide the length?

Padmanava asked

Answer:

18 gauge corresponds to a diameter of 1.22 mm

Therefore radius r1= 1.22/2=0.61 mm=0.00061m

10 gauge means diameter is 3.25 mm

Radius r2 = 3.25/2=1.625mm=0.001625m

Sine the resistance needs to be the same, we can use the formula


Which gives

As resistivity is same.

Substitute the values and you will get the answer.

Electric Field of Axons!

A nerve signal is transmitted through a neuron when an excess Na+ inos suddenly enters the axon, along cylindrical part of the neuron. Axons are approximately 10.0 micrometer in diameter, and measurements show that about 5.6×10^11 Na+ ions per meter ( each of charge e+)enter during this process. Although the axon is a long cylinder, the charge doesn’t all enter everywhere at the same time. A plausible model would be a series if point charges moving along the axon. Let us look at a 0.10-mm length of the axon and model it as a point of charge.

axons-are-long-protrusions-from-neurons-that-carry-nerve-impulses-to-other-nerve-cells-neurons_9
AXON

(a) If the charge that enters each meter of the axon gets distributed uniformly along it, how many coulombs of charge enter a 0.10-mm length of the axon?
(b) What electric field ( magnitude and direction) does the sudden influx of charge produce at the surface of the body if the axon is 5.00 cm below the skin?
(c) Certain sharks can respond to electric fields as weak as 1.0 microN/C. how far from this segment of axon could a shark be and still detect its electric field?

Current electricity – Numerical

A 10m length of aluminium wire has a diameter of 1.5mm. It carries a current of 12A. Find (i) the current density. (ii) the drift velocity (iii) the electric field in the wire. aluminium has approximately 10^29 free electrons per m^3

A numerical problem on Drift velocity

Two conducting wires X and Y of same diameter but different materials are joined in series across a battery . if the number density of electrons in X is twice that in Y . Find the ratio of drift velocity of electrons in the two wires.
(Adithya Singh asked this)

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