15. The

A copper wire and a tungsten wire of the same length have the same resistance. What is the ratio of the diameter of the copper w

spayn [35]

Answer:

Therefore the ratio of diameter of the copper to that of the tungsten is

$\sqrt{3} :\sqrt{10}$

Explanation:

Resistance: Resistance is defined to the ratio of voltage to the electricity.

The resistance of a wire is

directly proportional to its length i.e $R\propto l$
inversely proportional to its cross section area i.e $R\propto \frac{1}{A}$

Therefore

$R=\rho\frac{l}{A}$

ρ is the resistivity.

The unit of resistance is ohm (Ω).

The resistivity of copper(ρ₁) is 1.68×10⁻⁸ ohm-m

The resistivity of tungsten(ρ₂) is 5.6×10⁻⁸ ohm-m

For copper:

$A=\pi r_1^2 =\pi (\frac{d_1}{2} )^2$

$R_1=\rho_1\frac{l_1}{\pi(\frac{d_1}{2})^2 }$

$\Rightarrow (\frac{d_1}{2})^2=\rho_1\frac{l_1}{\pi R_1 }$ ......(1)

Again for tungsten:

$R_2=\rho_2\frac{l_2}{\pi(\frac{d_2}{2})^2 }$

$\Rightarrow (\frac{d_2}{2})^2=\rho_2\frac{l_2}{\pi R_2 }$ ........(2)

Given that $R_1=R_2$ and $l_1=l_2$

Dividing the equation (1) and (2)

$\Rightarrow\frac{ (\frac{d_1}{2})^2}{ (\frac{d_2}{2})^2}=\frac{\rho_1\frac{l_1}{\pi R_1 }}{\rho_2\frac{l_2}{\pi R_2 }}$

$\Rightarrow( \frac{d_1}{d_2} )^2=\frac{1.68\times 10^{-8}}{5.6\times 10^{-8}}$ [since $R_1=R_2$ and $l_1=l_2$ ]

$\Rightarrow( \frac{d_1}{d_2} )=\sqrt{\frac{1.68\times 10^{-8}}{5.6\times 10^{-8}}}$

$\Rightarrow( \frac{d_1}{d_2} )=\sqrt{\frac{3}{10}}$

$\Rightarrow d_1:d_2=\sqrt{3} :\sqrt{10}$

Therefore the ratio of diameter of the copper to that of the tungsten is

$\sqrt{3} :\sqrt{10}$

8 0

3 years ago

In a shipping company distribution center, an open cart of mass 50.0 kg is rolling to the left at a speed of 5.00 m/s. Ignore fr

spin [16.1K]

Answer:

a) $v_p=9.35m/s$

Explanation:

From the question we are told that:

Open cart of mass $M_o=50.0 kg$

Speed of cart $V=5.00m/s$

Mass of package $M_p=15.0kg$

Speed of package at end of chute $V_c=3.00m/s$

Angle of inclination $\angle =37$

Distance of chute from bottom of cart $d_x=4.00m$

a)

Generally the equation for work energy theory is mathematically given by

$\frac{1}{2}mu^2+mgh=\frac{1}{2}mv_p^2$

Therefore

$\frac{1}{2}u^2+gh=\frac{1}{2}v_p^2$

$v_p=\sqrt{2(\frac{1}{2}u^2+gh)}$

$v_p=\sqrt{2(\frac{1}{2}v_c^2+gd_x)}$

$v_p=\sqrt{2(\frac{1}{2}(3)^2+(9.8)(4))}$

$v_p=9.35m/s$

4 0

2 years ago

A cannon is shot downwards with an initial speed of 10m/s at an angle of 20 degrees South of East off a 60m cliff. Find the init

Sliva [168]

Answer:hmm

Explanation:

7 0

3 years ago

Alice kicks a 0.25 kg soccer ball with 0.5 N of force. What force does the ball exert on Alice’s foot as she kicks it

Lelechka [254]

You do not doubt it. The third Law of Newton really works. I would say it is the most reliable law of the Universe. Action and reaction. It is not subject to special conditions, it works always. If an object exerts a force over other object, the second object exerts a force of equal magnitude but in the opposed direction over the first.

So, the answer, undoubtedly, is that the ball exerts a force of 0.5 N over Alices's foot as she kicks it.

7 0

3 years ago

Read 2 more answers

Two objects are made of the same material, but they have different masses and temperatures. If the objects are brought into ther

DIA [1.3K]

The smaller body will have greater temperature change.

<h3><u>Explanation</u>:</h3>

Temperature is defined as the degree of hotness or coldness of a body. The relationship of the temperature with heat is described as

Q =m c dT.

Where Q is the heat content

m is the mass of body

c is the specific heat of body

dT is the temperature change of body.

Here the bodies are made up of same substance, so specific heat is same. The mass of bigger body is M and smaller body is m.

So the temperature change of the body will be dependent on the mass of the body. Heat loss by one body will be equal to heat gained by the other.

So M dT1 = mdT2.

So, M/m = dT2 / dT1.

So the the smaller body will be suffering higher temperature change.

3 0

3 years ago