Two objects, C & D, have the same momentum. Object C has ½ the mass of object D. Find the value of the ratio of velocity C to velocity D.

Part 2
Find the value of the ratio of kinetic energy C to kinetic energy D. 

The Modified Mercalli scale is used measures the amount of damage done during an earthquake. This helps to locate the epicenter of the earthquake.  It depicts the intensity of the earthquake based on the damage occurred due to the earthquake. The responses from many people who experienced the earthquake are collected by the scientists, assigned a value and plotted on a map

The plotted number can change with the reference place within the region of disturbance. It depends on the location of the observer with reference to the epicenter of the earthquake. The reporting depends on the witness. Some can exaggerate the extent of damage caused. All  the above mentioned are possible sources of error  when using the Modified Mercalli scale to locate the earthquake's epicenter.

After being thrown downwards from a high building with an initial velocity of 3.0 m/s, and accelerating in free fall for 2.0s, the velocity of the ball would be 22.6 m/s.

The student throws a ball downwards with an initial velocity of 3.0 m/s. In a situation of free fall, the object accelerates due to gravity, which is approximately 9.8 m/s² on Earth's surface. As the ball is being thrown downwards, the gravitational acceleration would add to the initial velocity.

We can use the equation v = u + at to find the velocity of the ball after a certain time where:
v = final velocity
u = initial velocity
a = acceleration
t = time
The initial velocity (u) here is 3.0 m/s, acceleration (a) is 9.8 m/s² (as the object is in free fall), and time (t) is 2.0s (as given).

So substituting these values in the equation, we get:
v = 3.0 m/s + (9.8 m/s² * 2.0s) = 3.0 m/s + 19.6 m/s
This sums up to a final velocity (v) of 22.6 m/s. Therefore, the ball's velocity after 2.0 seconds is 22.6 m/s.

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Answer:

hypotenuse² = base² +height²

Explanation:

Let us suppose a right angled triangle having b as base, h as hypotenuse and p as perpendicular distance.

The relation between the length of legs, the base and the hypotenuse is called Pythagoras theorem. It is given by :

[tex]h^2=b^2+p^2[/tex]

or

hypotenuse² = base² +height²

Answer:

The relation between the length of the hypotenuse in a right triangle and  lengths of the legs is [tex]H^{2} = p^{2}+b^{2}[/tex].

Explanation:

The legs of right angled triangle is also known as perpendicular and base respectively.

Let p be length of perpendicular and b be the length of base. Then by Pythagoras theorem,

[tex]H^{2} = p^{2}+b^{2}[/tex]

here, H is the length of Hypotaneous.

Thus, relation between the length of the hypotenuse in a right triangle and  lengths of the legs is [tex]H^{2} = p^{2}+b^{2}[/tex].

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Answer: Option C

Explanation: The carbon dioxide is major green house gas that traps heat. But due to global warming the amount of carbon dioxide in the environment is increasing day by day.

The carbon dioxide gets in the ocean water and harms the organisms present in the ocean water. The coral present inside the water covers a very large area and is a major part of the marine ecosystem.

The carbon dioxide in excess leads to coral bleaching. This is a phenomenon in which the algae that is found inside the coral leaves the coral due to stress condition.

Thus, carbon dioxide in water increase the acidification in ocean which leads to coral bleaching.

The time it would take for the sound wave to travel to a subject 3.42m away and back, with a sound speed of 343 m/s, is approximately 0.01995 seconds.

The time it takes for the sound wave to return to the camera can be found by applying the equation distance = speed * time. This principle is often utilized in technologies such as sonar and ultrasound imaging. Here the distance is doubled since the sound has to travel to the subject and back to the camera. If the subject is 3.42 m away, the total distance covered by the sound wave is 3.42m * 2 = 6.84m. Given that the speed of sound is 343 m/s, we can rearrange the equation to solve for time: time = distance/speed. Hence, time = 6.84m / 343 m/s = 0.01995 s, rounded to 5 decimal places.

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It takes 0.02 seconds for the sound wave to return to the camera if the subject were 3.42 metres away.

The given question can be solved by simple use of kinematic equations. It is given that the camera determines the distance to the subject by sending out a sound wave. The speed of the sound wave is v = 343 m/s

Now, for a subject at a distance of 3.42 metres away the sound wave has to travel to the subject and travel back to the camera as well. Therefore the total distance covered by the sound wave will be twice the distance of the subject from the camera.

d = 2 × 3.42 m = 6.84 m

From the kinematic equation;

[tex]v = \frac{d}{t}[/tex], where t = time taken

rearranging for t, we get:

[tex]t = \frac{d}{v}[/tex]

substituting the values,

[tex]t = \frac{6.84 m}{343 m/s}[/tex]

or, t = 0.019 s ≈ 0.02 s

The mass of the rock is equal to 5 Kg when its weight is 49 N.

The weight of a body can be described as the force acting on the body due to gravity. Weight can be described as a vector parameter if gravity is acting on the object.

The S.I. unit for measurement weight is of force, which S.I. is the newton (N). A body with a mass of 1 kg has a weight of about 9.8 Newton on the surface of the Earth, and about 1/6 as much on the Moon.

The mathematical expression to find the weight of an object is written as follows:

W = mg

Given the weight of the rock, W = 49 N

The acceleration due to gravity on the rock, g = 9.8 m/s²

The mass of the rock on the earth will be equal to:

49 = m × 9.8 m/s²

m = 5 kg

Therefore, the mass of the rock is equal to 5 kg.

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Answer: 1. B) 720 N

2. D) 2500 m

3. D) 408 Hz

4. C) 4m

5. A) 246 hz

6. D) 31st

7. B) the frequency of the sound is 100 Hz

8. C) 0.78 m

9. B) 16 Hz

10. B) 311 m/s

Kinetic energy of a moving body can be calculated from mass and velocity. The kinetic energy of the cycler with a velocity of 3.4 m/s and mass of 30 Kg is 173 J or 1.7 × 10² joules.

Kinetic energy is form of energy formed by virtue of the motion of a body. It is directly proportional to the mass and square of the velocity of the body. The equation of kinetic energy can be written as follows:

KE = 1/2 mv²

When a body starts to move its kinetic energy starts to increase whereas, potential energy gets declined. As per the above relation, the kinetic energy of a body doubles when the mass is doubled. If the velocity is doubled, kinetic energy will increases by four times.

It is given that the combined mass of the cycle and the girl is 30  Kg and the velocity is 3.4 m/s. Kinetic energy can be calculated as follows:

KE = 1/2 30 × ( 3.4 )²

    = 173 J.

Therefore, kinetic energy of the cycler with a velocity of 3.4 m/s and mass of 30 Kg is 173 J or 1.7 × 10² joules and option a is correct.

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Final answer:

According to Ohm's law, since circuit A has a resistor four times larger than circuit B and both have identical voltage sources, the current in circuit A is one fourth as large as in circuit B.(Option D)

Explanation:

If two circuits have identical voltage sources and resistors and the resistance in circuit A is four times as large as the resistance in circuit B (RA = 4RB), we can apply Ohm's law (V = IR) to determine the relationship between the currents in each circuit. Since the voltage (V) across both circuits is the same, and the resistance (R) is four times higher in circuit A compared to circuit B, the current in circuit A will be four times smaller than the current in circuit B. Ohm's law rearranged to solve for current (I) is I = V/R.

Therefore, with a higher resistance in circuit A, the current is inversely proportional to the resistance. Hence, the correct statement is:

The current flowing through circuit A is one fourth as large as the current flowing through circuit B (Option D).

Energy cannot be created nor be destroyed. But it can change from on from one form to the other. The total energy in a system always remains a constant.

What is conservation of energy?

According to the law of conservation of energy, energy can neither be created nor be destroyed. Therefore, the total energy of a system remains constant.

However, one form of energy can be converted to other form. There are different kinds of energy generating from different sources. Kinetic energy, potential energy, nuclear energy, gravitational energy, thermal energy, chemical energy, light energy etc. are different forms of energy.

In battery or cell the chemical energy is converted to electrical energy. Similarly in a solar cell light energy is converted to electrical energy. Whereas, in all electrical devices such as fan, motors, etc electrical energy is converted to the mechanical energy.

In this way the total energy of the system is always maintained on itself without any loss or gain in amount. Therefore,  the total amount of energy before and after any energy transformations remain the same to balance the system.

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Answer:

C

Explanation:

Because the north and the south pole are like the earth if they didn't attracted  we would all die.

Magnetic fields have north and south magnetic poles. This statement best describes magnetic fields. So, option(C) is correct.

In the presence of a magnet, an electric current, or a shifting electric field, there is a vector field called a magnetic field where magnetic forces can be seen.

Electric charges in motion and the intrinsic magnetic moments of elementary particles connected to the fundamental quantum characteristic known as spin create a magnetic field.

As parts of the electromagnetic force, one of the four fundamental forces of nature, magnetic field and electric field are interdependent.

In magnetic field, there always be a north pole and a south pole because magnetic monopole doesn't exists. So, option (C) is correct.

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Final answer:

The units of specific heat, which indicate the amount of energy needed to raise the temperature of 1 g of a substance by 1°C, are joules per kilogram Kelvin (J/(kg·K)) or joules per kilogram degree Celsius (J/(kg·°C)) in the SI system, and calories (cal) in non-SI units.

Explanation:

The units of specific heat are an important aspect in understanding how much energy is required to change the temperature of a substance. The specific heat of a substance is the amount of energy needed to increase the temperature of 1 gram of the substance by 1°C. In the International System of Units (SI), the unit of specific heat is joules per kilogram Kelvin (J/(kg·K)) or joules per kilogram degree Celsius (J/(kg·°C)). Additionally, the non-SI unit called the calorie (cal) is sometimes used, where 1 calorie is the energy required to raise the temperature of 1 gram of water by 1°C.

It's important to note that the value of specific heat remains the same whether measured in J/(kg·K) or J/(kg·°C), since the temperature change is the same whether expressed in Kelvin or degrees Celsius. For practical and historical reasons, other units like the calorie and the kilocalorie (kcal) are also used, particularly in contexts like food energy where 'calories' commonly refer to kilocalories.