You are given two converging lenses to build a compound microscope. Lens A has focal length 0.50 cm and lens B has focal length of 3.0 cm. Which one of the two lenses would you use for the objective

Solution :

We know that the volume of sphere is given by :

[tex]$V=\frac{4}{3}\pi r ^3$[/tex]

Given r = 50 mm

The density of copper is :

[tex]$\rho_c = 8910 \ kg/m^3$[/tex]

The density of steel is :

[tex]$\rho_s = 7830\ kg/m^3$[/tex]

Therefore, mass of copper is :

[tex]$m_c= V . \rho$[/tex]

[tex]$m_c= \frac{4}{3} \pi (0.05)^3 \times 8910$[/tex]

     = 4.665 kg

     = 4665 g

Similarly, mass of steel is :

[tex]$m_s= V . \rho$[/tex]

[tex]$m_s= \frac{4}{3} \pi (0.025)^3 \times 7830$[/tex]

     = 0.512 kg

     = 512 g

Now the distance between the centers of the particles is by Pythagoras theorem,

[tex]$l^2=(4r)^2+(2r)^2$[/tex]

l = 4.472 x r

 = 4.472 x 50

 = 224 mm

 = 0.224 m

From the law of gravitation,

We know,  [tex]G = 6673 \times 10^{-11} \ m^3 / kg-s^2[/tex]

∴  [tex]$F=G\times \frac{m_c \times m_s}{l^2}$[/tex]

[tex]$F=6.673 \times 10^{-11}\times \frac{4.665 \times 0.512}{(0.224)^2}$[/tex]

[tex]$F = 3.176 \times 10^{-9} \ N$[/tex]

Now,

[tex]$\alpha = \tan^{-1} \left( \frac{2r}{4r}\right)$[/tex]

   =  [tex]$26.56^\circ$[/tex]

Therefore, we can write it in the vector form as

[tex]$\text{F}=F(-i . \cos \alpha - j. \sin \alpha)$[/tex]

[tex]$\text{F}=3.176 \times 10^{-9}(-i . \cos 26.56 - j. \sin 26.56)$[/tex]

[tex]$\text{F}=(-2.840\ i- 1.420 \ j) \times 10^{-9} \ N$[/tex]

Answer:

To prevent our clothes from dust, dirt, spills and debris during cooking, serving, cleaning or performing a creative task. Aprons protect your clothes and acts as a protective barrier.

Answer:

Explanation:

According to the Law of Momentum Conservation, what happens after the collision has to equal what happened before the collision because momentum cannot be created nor destroyed; it has to go somewhere else. Like energy eventually dissipates into heat. The equation for this is:

[tex][m_Av_A+m_Bv_B)]_b=[(m_Av_A+m_Bv_B)]_a[/tex] and filling in our info, calling right positive and left negative:

[(24(3.2) + 32(-12.8)] = [(24(-2.9) + 32(vB)] and

[(77 - 410)] = [(-7.0 × 10¹ + 32vB)] and

-330 = -7.0 × 10¹ + 32vB and

-260 = 32vB so

vB = -8.1 m/s Thus, cart B is moving to the left at a velocity of 8.1 m/s

(I used the rules for sig dig very intentionally and correctly; I'm not sure how strict your teacher is about them. I require my students to use the rules to perfection, as I did here.)

Answer:

what is the upwards force?

Answer:

final velocity=-49m/s and height=122.5

Explanation:

u=0,t=5s,v=?

v=u+gt

v=0+(-9.8)5

v=-49m/s

h=ut+1/2gt*2

h=0(5)±1/2(-9.8)5*2

h=-122.5 or 122.5

but height=122.5 because height cannot be negative

Explanation:

The answer is (B). The speed of light is the same for all observers regardless of their motion relative to the light source.

The speed would an observer on Earth measures for the light from the spotlight will be 3×10⁸ m/sec.

Speed is defined as the rate of change of the distance or the height attained. it is a time-based quantity. it is denoted by u for the initial speed while v for the final speed. its si unit is m/sec.

The given data in the problem is;

The speed of light is, [tex]\rm C =3 \times 10^8\ m/sec[/tex]

All frames of reference have the same speed of light in a vacuum. Therefore the speed would an observer on Earth measures for the light from the spotlight will be 3×10⁸ m/sec.

Hence option B is correct.

To learn more about the speed refer to the link;

https://brainly.com/question/7359669

Explanation:

In 1911, Marie was awarded a second Nobel Prize in Chemistry for her discovery of the elements polonium and radium. In honor of the 100-year anniversary of her Nobel award, 2011 was declared the "International Year of Chemistry."

Answer:

Explanation:

Angular momentum has a formula of L = mvr. Fillingin:

L = (1.0)(5.0)(1.0)

L = 5.0 kg*m/s

Answer:

I think there's a pdf for the questions you need

WorksheetKineticVsPotentialEnergy.pdf

Explanation:

Answer:

0.893 rad/s in the clockwise direction

Explanation:

From the law of conservation of angular momentum,

angular momentum before impact = angular momentum after impact

L₁ = L₂

L₁ = angular momentum of bullet = + 9 kgm²/s (it is positive since the bullet tends to rotate in a clockwise direction from left to right)

L₂ = angular momentum of cylinder and angular momentum of bullet after collision.

L₂ = (I₁ + I₂)ω where I₁ = rotational inertia of cylinder = 1/2MR² where M = mass of cylinder = 5 kg and R = radius of cylinder = 2 m, I₂ = rotational inertia of bullet about axis of cylinder after collision = mR² where m = mass of bullet = 0.02 kg and R = radius of cylinder = 2m and ω = angular velocity of system after collision

So,

L₁ = L₂

L₁ = (I₁ + I₂)ω

ω = L₁/(I₁ + I₂)

ω = L₁/(1/2MR² + mR²)

ω = L₁/(1/2M + m)R²

substituting the values of the variables into the equation, we have

ω = L₁/(1/2M + m)R²

ω = + 9 kgm²/s/(1/2 × 5 kg + 0.02 kg)(2 m)²

ω = + 9 kgm²/s/(2.5 kg + 0.02 kg)(4 m²)

ω = + 9 kgm²/s/(2.52 kg)(4 m²)

ω = +9 kgm²/s/10.08 kgm²

ω = + 0.893 rad/s

The angular velocity of the cylinder bullet system is 0.893 rad/s in the clockwise direction-since it is positive.

Answer:

C. mg sin(θ)

Explanation:

The plane is incline and the only force acting in the object is the gravity, so you multiply mg per sin(θ) because sin(θ) gave you the part of the gravity acting in the horizontal direction parallel with the inclined surface

The expression shows the net force on the object along the surface of the incline is mg sin(θ).  The correct option is C.

When two or more forces are acting on the system of objects, then the to attain equilibrium, net force must be zero.

An object of mass m slides down an incline with angle (θ).

The plane is incline and the only force acting in the object is the gravity, The weight or gravity acting in the horizontal direction parallel with the inclined surface is  mg sin(θ).

Thus, the correct option is C.

Learn more about net force.

https://brainly.com/question/18031889

#SPJ2

Answer: See answers below.

Explanation: In this problem, we must be clear about the concept of weight. Weight is defined as the product of mass by gravitational acceleration.

We must be clear that the mass is always preserved, that is, the mass of 15 [kg] will always be the same regardless of the planet where they are.

where:

W = weight [N] (units of Newtons)

m = mass = 15 [kg]

g = gravity acceleration [m/s²]

Since we have 9 places with different gravitational acceleration, then we calculate the weight in each of these nine places.

Mercury

Venus

Moon

Mars

Jupiter

Saturn

Uranus

Neptune

Pluto

In this problem, we must be clear about the concept of weight. Weight is defined as the product of mass by gravitational acceleration.

We must be clear that the mass is always preserved, that is, the mass of 15 [kg] will always be the same regardless of the planet where they are.

where:

W = weight [N] (units of Newtons)

m = mass = 15 [kg]

g = gravity acceleration [m/s²]

Since we have 9 places with different gravitational acceleration, then we calculate the weight in each of these nine places.

Mercury

Venus

Moon

Mars

Jupiter

Saturn

Uranus

Neptune

Pluto

Answer:

A

Explanation:

A. The Moon orbits the Earth, and the Earth-Moon system orbits the Sun

B. The Earth and Moon both orbit the Sun separately

C. The Sun orbits the Earth-Moon system

D. The Moon revolves around Earth but not the Sun

Answer:

Jan Hendrik Schön I believe

Answer:

The high pressure areas in a longitudinal wave are called compressions.

Explanation:

The critical velocity is that velocity of liquid flow, up to which its flow is streamlined (laminar)& above which its flow becomes turbulent. It's denoted by Vc & it depends upon: Coefficient of viscosity of liquid (η) Density of liquid. Radius of the tube.

Liar, not even 40 points....

Answer:

The answer is true. This is correct.

Answer:

4 kg → +4 m/s

5 kg → -5 m/s

Explanation:

The law of conservation of momentum states that:

You'll notice that we have two missing variables: v₁' & v₂'. Assuming this is a perfectly elastic collision, we can use the conservation of kinetic energy to set the initial and final velocities of the individual bodies equal to each other.

Let's substitute all known variables into the first equation.

Let's substitute the known variables into the second equation.

Now we have a system of equations where we can solve for v₁ and v₂.

Use the elimination method and multiply the bottom equation by -4.

Add the equations together.

The final velocity of the second body (5 kg) is -5 m/s. Substitute this value into one of the equations in the system to find v₁.  

The final velocity of the first body (4 kg) is 4 m/s.

We can verify our answer by making sure that the law of conservation of momentum is followed.

The combined momentum of the bodies before the collision is equal to the combined momentum of the bodies after the collision. [✓]

Answer:

The correct option is C) III. That is, the trout will suffer from disease.

Explanation:

Note: This question is not complete as the options are not included. The complete question with the options is therefore provided before answering the question as follows:

A lake is home to a large number of trout. Identify what is most likely to happen if a chemical is dumped into the lake.

I. The trout will not be affected by the pollution.

II. The number of trout will increase.

III. The trout will suffer from disease.

A) I

B) I and II

C) III

D) II and III

The explanation of the answer is now provided as follows:

Natural selection is the process that took place in the lake. Only those trouts that were fit to survive, or those that have alleles that allow them adapt to new conditions, live and multiply in the presence of an external environmental effect like pollution. In such a circumstance, the fittest organisms would have survived, and the population's allelic frequency would have grown through time. Due to pollution, creatures harboring the other alleles died, causing the total frequency of alleles to alter.

Therefore, the correct option is C) III. That is, the trout will suffer from disease.

Answer:

This is the twin paradox.

Answer:

From butter in croissants to cocoa solids in chocolate, edible fats pack a flavor punch that delights like no other macronutrient we consume. Fats are the most energy dense macronutrients, providing more than twice as many kilocalories per gram as proteins or carbohydrates, which may be the reason we've developed a taste for them.

Explanation:

Answer;

The mass value for the above kinetic energy equation is 400.0000 kg. This is equal to:

■ 400,000.0000 g.

■ 14,109.6000 ounces.

■ 881.8480 pounds.

I hope you understand....

Answer:

Static Electricity

Explanation:

I think this is what your asking

Answer:

a nail

Explanation:

Answer:

crude oil, natural gas, coal, and uranium. These are all resources that are processed into products that can be used commercially.

Explanation:

9 ounces bc if he does then he wont be so like ugh I'm out of wonder land yeah 9 ounces deffo

Solution :

A) Electric current is the flow of electrons .

B) We know, by ohm's law :

V = I × R

Putting given values in above equation, we get :

V = 0.56 × 72 V

V = 40.32 V

Hence, this is the required solution.

Answer:

The parent nucleus splits into lighter daughter elements

Explanation:

Nuclear fission involves the splitting of nucleus of a lighter element with smaller particles