The figure below shows a ball on a curved surface. The ball is released at point A. At which point does the ball have maximum gravitational potential energy?

Answer:

0.545g/cm OR 545kg/m(both answers are in cubic)

Explanation:

first we have to find mass of liquid x

mass= density × volume

=25 cubic centimetre × 1.2g/cm

=3g

liquid y= density × volume

=30 cubic centimetre × 0.9g/cm

= 27g

next,we add the two masses

27+3

30g(mass of the whole mixture)

formula for finding density of the mixture

Mass1+ Mass2 ÷ Volume 1+ volume 2

30g ÷55 cubic centimetre

the answer will be a recurring decimal and as we know,we write decimals in 3 significant numbers so we round off

0.5454g/cm= 0.545g/cm and in SI units it's

545kg per cubic meter

Let [tex]\vec u[/tex] and [tex]\vec v[/tex] be the vectors, and let [tex]x=\|\vec u\|=\|\vec v\|[/tex] be their common magnitude.

The resultant [tex]\vec u + \vec v[/tex] is [tex]\sqrt 2[/tex] times larger in magnitude than either vector alone, so [tex]\|\vec u+\vec v\| = \sqrt2\,x[/tex].

Recall the dot product identity

[tex]\vec a \cdot \vec b = \|\vec a\| \|\vec b\| \cos(\theta)[/tex]

where [tex]\theta[/tex] is the angle between the vectors [tex]\vec a[/tex] and [tex]\vec b[/tex]. In the special case of [tex]\vec a=\vec b[/tex], we get

[tex]\vec a \cdot \vec a = \|\vec a\|^2 \cos(0^\circ) \implies \|\vec a\| = \sqrt{\vec a\cdot\vec a}[/tex]

Now, to get the angle between [tex]\vec u[/tex] and [tex]\vec v[/tex], we have

[tex]\vec u \cdot \vec v = \|\vec u\| \|\vec v\| \cos(\theta) \implies \cos(\theta) = \dfrac{\vec u \cdot \vec v}{x^2}[/tex]

To compute the dot product, we take the dot product of the resultant with itself.

[tex](\vec u+\vec v) \cdot (\vec u + \vec v) = \|\vec u + \vec v\|^2[/tex]

Solve for [tex]\vec u\cdot\vec v[/tex].

[tex](\vec u\cdot\vec u) + 2(\vec u\cdot\vec v) + (\vec v\cdot\vec v) = \|\vec u + \vec v\|^2[/tex]

[tex]\|\vec u\|^2 + 2(\vec u\cdot \vec v) + \|\vec v\|^2 = \|\vec u+\vec v\|^2[/tex]

[tex]x^2 + 2(\vec u \cdot \vec v) + x^2 = (\sqrt2\,x)^2[/tex]

[tex]2(\vec u\cdot\vec v) + 2x^2 = 2x^2[/tex]

[tex]2(\vec u\cdot\vec v) = 0[/tex]

[tex]\vec u\cdot\vec v = 0[/tex]

Since their dot product is zero, [tex]\vec u[/tex] and [tex]\vec v[/tex] are perpendicular, so [tex]\theta=90^\circ[/tex].

A gold leaf electroscope's cap develops a negative charge when a negatively charged rod is brought close to it; the case is then grounded, creating a negative charge in the leaf. Option D is correct.

When the matter is put in an electromagnetic field, it has an electric charge, which causes it to experience a force. A positive or negative electric charge can exist.

Similar charges repel each other, whereas dissimilar charges attract each other.

The term "neutral" refers to an item that has no net charge. A charge is something experienced as a force in the electric and magnetic fields.

When a negatively charged rod is brought near the cap of a gold leaf electroscope whose case ad then is earthed, then the leaf has an induced negative charge.

Hence option D is correct.

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The frequency of oscillation on the frictionless floor is 28 Hz.

The frequency of the oscillation is calculated as follows;

f = (1/2π)(√k/m)

where;

f = (1/2π)(√7580/0.245)

f = 28 Hz

Thus, the frequency of oscillation on the frictionless floor is 28 Hz.

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The magnetic flux associated with the coil is 0 Wb.

Magnetic flux is the total magnetic field that travels through a specific location.

It is a very useful tool for explaining the effects of magnetic force on things in a specific location.

The magnetic flux measurement is location specific.

The magnetic flux through the coil is NBA cosα

where N is number of turns, B is Magnetic field, A is area of coil and α is the angle between normal to the area of coil and the direction of magnetic field.

Magnetic Flux = NBA cosα

We have given number of turns as 100, magnetic field as 3 and area as 5 m².

Also, the value of α will be 90°

Magnetic Flux = NBA cosα Wb

Magnetic Flux = 100 × 3 × 5 × cos90° Wb

Magnetic Flux = 100 × 3 × 5 × 0 Wb

Magnetic Flux = 0 Wb

So we can conclude that the magnetic flux through the coil is 0 wb after applying the above concept.

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From the calculation,  the man has an average velocity of 1.25 m/s.

The man travelled a total distance = 100 m

We know that;

1 complete cycle = 4 s

Then

 20 complete cycle = ?

= 20 x 4 s

= 80 s

So we can find the average velocity from;

Average velocity = 100 m/80 s

Average velocity = 1.25 m/s

Hence, the man has an average velocity of 1.25 m/s.

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No, it is not valid because they did not have any repeat trials.

The acceleration that an object experiences as a result of gravitational force is referred to as the object's acceleration due to gravity. M/s2 is its SI unit. Gravitational acceleration is a vector quantity, which means it has both a magnitude and a direction. The letter g stands for the acceleration due to gravity at Earth's surface. Its standard value is 9.80665 m/s2 (32.1740 ft/s2), according to the formula. A body in free fall actually accelerates differently depending on the location.

Because moving the object, air, or other factors could distort the results of a single instance. There must therefore be repeated experiments in order to obtain precise results.

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Answer: A 3600 kg boat is moving with a speed of 2.4 m/s. A much smaller 100 kg jet ski has the same amount of kinetic energy. The is the speed of the jet ski is 14.4 m/s².

Explanation: To find the correct answer to the question given, we need to know more about the Kinetic energy.

                        [tex]KE=\frac{1}{2} mv^2[/tex]

                        [tex]\frac{1}{2}m_1v_1^{2} =\frac{1}{2}m_2v_2^2\\ Thus, \\v_2^2=\frac{m_1v_1^{2}}{m_2} =207.36\\v_2^2=14.4 m/s^2[/tex]

Thus, we can conclude that, the is the speed of the jet ski is 14.4 m/s².

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Answer:

M g H = 1/2 M v^2       potential energy = kinetic energy

v^2 = 2 g H = 2 * 9.80 * 6 = 117.6 m/s^2

v = 10.8 m/s    

(C)

The speed of the cat 5 m from the sidewalk is 7.42 m/s

What is speed:

The Newton's equation of motion:

here the cat falls from the height,

h = 40 m

since The cat is falling from rest

Initial velocity, u = 0 m/s

acceleration, a = g = 9.8 m/s^2

substituting values in eq.

40 = 0 + ( 9.8 t^2)

t^2 = 40 / 9,8

t^2 = 4.0814

t = 2.02 s

now when cat is 5 m from sidewalk

distance, S = 40 - 5 = 35 m from top

so,

35 = u*2.02 + 1/2 ( 9.8* 2.02^2 )

u = 15 / 2.02

u = 7.4257 m/s

The speed of the cat 5 m from the sidewalk is 7.42 m/s

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Kinetic energy of the pile driver is 10 KJ.

To find the answer, we need to know about the conservation of mechanical energy.

Conservation of mechanical energy says that the total energy of a system remains same during a process.

Thus, we can conclude that the increased kinetic energy is 10KJ.

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Solar energy and Hydro is the correct option.

Today's energy supply is provided by solar energy and Hydro as compared to our ancestors because our ancestors have no modern technology to obtain energy from sun and water. They get energy from burning of fossil fuels and biomass.

So we can conclude that solar energy and Hydro is the correct option.

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Answer:

acceleration, a = 11m/s² ; time, t = 0.84sec

Explanation:

Fw = mass(m) × acceleration due to gravity(g)

Fw = 71.9kg × 10m/s²

Fw = 719N

F = Fw(sintheta+coefficient of friction(costheta))

F = 719(sin38° + 0.61(cos38°)

F = 719(0.615661475+0.480686559)

F = 719(1.096348034)

F = 788.27N

Force(F) = mass(m) × acceleration(a)

Make acceleration the subject

acceleration = Force÷ mass

a = 788.27÷719

a = 11m/s²

using this formula v² = u² +2gh

v² = 0² + 2×10m/s²×4.3m

√v² = √86

v = 9.27m/s

acceleration = velocity/time

make time the subject

time = velocity/acceleration

t = 9.27m/s/11m/s²

t = 0.84sec

Answer:

Pakistan has low rates of non renewable energy thus it is mandatory that the renewable resources be put into use. The vast deserts in punjab and sindh should be used to set up solar panels and the coastal areas of sindh and balochistan should be used as wind power. The northern areas have melting glaciers and high precipitation rates rates thus HYDEL power should be used in the form of dams

Answer:

(I) 49m/s

(ii) 122.5m

Explanation:

Data obtained from the question include:

Time (t) = 5 s

Acceleration due to gravity (g) = 9.8 m/s²

Time (t) = 4 s

Acceleration due to gravity (g) = 9.8 m/s²

v = gt

v = 5× 9.8

v = 49 m/s

Thus, the brick's velocity after 4 s is 49m/s

B. Determination of how far the brick fall in 5 s.

Time (t) = 5 s

Acceleration due to gravity (g) = 9.8 m/s²

Height (h) =?

h = ½gt²

h = ½ × 9.8 × 5²

h = 5× 16

h = 122.5 m

Thus, the brick fall 122.5m during the time.

In order to determine the kinetic energy of a body, it is important to ask about the mass and velocity of the body.

Kinetic energy is the energy a body possesses due to the motion of that body.

The equation to calculate kinetic energy of a body is given as:

[tex]KE = \frac{1}{2}mv^{2}[/tex]

where

Therefore, it is important to ask what the mass of a body is and the speed at which it is moving in order to determine the kinetic energy of the body.

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The question is incomplete. Please read below the missing content.

B) The 4 terrestrial planets have to as soon as were hot sufficient to be molten (like a liquid).

Terrestrial planets may be described as any planet of the sun machine or any exoplanet that is "Earth-like" in the experience that it is composed primarily of metals and rock, in evaluation to a planet that's a fuel large.

In the sun machine, the terrestrial planets are the inner planets closest to the solar, i.e. Mercury, Venus, Earth, and Mars.

Scientists believe that the densest, heaviest substances are at the center and not evenly allotted can be due to the truth that they need to once be warm enough to be molten. In this example, density will take region, making the heavier below and the lighter on the pinnacle.

In the four terrestrial planets, the densest, heaviest materials are at the center and not evenly distributed throughout the planet. Scientists interpret this observation to mean that:

a.the four terrestrial planets must once have been inside the Sun

b.the four terrestrial planets must once have been hot enough to be molten (like a liquid)

c.the four terrestrial planets must have formed where Jupiter and Saturn now are

d.the four terrestrial planets must have collided with each other many times

e.none of the above

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Scurvy and rickets are micronutrient deficiency diseases due to a lack of certain vitamins or minerals in the diet. Scurvy is caused by vitamin C deficiency and rickets by vitamin D.

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Answer:

Mechanical vs. Quartz Watch Movements

Mechanical watch movements are powered by gears and springs. They're autonomous little machines without the need for electric power sources, whereas quartz watches are powered by batteries that vibrate little crystals.

CR​ < CY​ < CB​

The factors which affect the critical angle are

(a) The colour (or wavelength) of light

(b) The temperature

(i) Effect of colour of light: The critical angle for a pair of media is less for the violet light and more for the red light. Thus the critical angle increases with the increase in wavelength of light.

(ii) Effect of temperature: The critical angle increases with increase in temperature because on increasing temperature of medium, its refractive index decreases.

According to the question,

μ 1​ sinCR​ =1

μ 2​ sinCY =1

μ 3​ sinCB​ =1

μ 1​ > μ 2​  and μ 2​ > μ 3

⟹μ 1​ > μ 2​ > μ 3

CR​ < CY​ < CB​

Thus,

The critical angle increases with the increase in wavelength of light.

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Vertical force on left support = 2891 N

Vertical force on right support = 1323 N

Let's assume the Length of the horizontal beam = L(see diagram)

Mass of beam (m) = 110kg

Mass of piano(M) = 320kg

Weight of the Horizontal beam(W1) =mg = 110×9.8= 1078N

Net force acting on the beam =0

[tex]F_{L}[/tex] - Mg - mg + [tex]F_{R}[/tex] = 0

[tex]F_{L}[/tex] = Force support to the left

[tex]F_{R}[/tex] = Force support to the right

τ = F×r where, τ= Torque

Net torque is also 0

[tex]F_{R}[/tex]L - Mg[tex]\frac{L}{4}[/tex] - mg[tex]\frac{L}{2}[/tex] =0

[tex]F_{R}[/tex] = ([tex]\frac{M}{4} + \frac{m}{2}[/tex])g = 1323 N

[tex]F_{L}[/tex] = (M + m)g - [tex]F_{R}[/tex] = 2891 N

Hence Vertical force on left support is 2891 N and on right support is 1323 N

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The toddler's change in velocity in metres per second is 1.68 m/s

To answer the question, we need to know what acceleration is

Acceleration is the change in velocity of an object with time. It is given by

a = Δv/Δt where

Making Δv subject of the formula, we have

Δv = aΔt

Since the toddler's accleration is 0.24 m/s² and got up from a nap and ran for 7.0 seconds,

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

Δv = aΔt

Δv =  0.24 m/s² × 7.0 s

Δv =  1.68 m/s

So, the toddler's change in velocity in metres per second is 1.68 m/s

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The speed of Sammy, given that he expends 1750 J while jogging is 7.1 m/s

The speed of Samnmy can be obtained as illustrated below:

E = ½mv²

1750 = ½ × 69.5 × v²

1750 = 34.75 × v²

Divide both side by 34.75

v² = 1750 / 34.75

Take the square root of both side

v = √(1750 / 34.75)

v = 7.1 m/s

Thus, Sammy is moving with a speed of 7.1 m/s

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The answer is W = 1.06 MJ.

Now develop and express of Force required:

                                            F = p*V*g

                                            F = 1000*(2*0.5*x*8*dx)*g

                                            F = 78480*x*dx

- Now, the work done is given by:

                                   W = F.s

Where s is the distance from the top of the hose to the differential volume:

                                        s = (5 - x)

We have the work as follows:

                              dW = 78400*x*(5-x)dx

Now integrate the following express from 0 to 3 till the tank is empty:

 W = 78400*(2.5*x^2 - (1/3)*x^3)

 W = 78400*(2.5*3^2 - (1/3)*3^3)

 W = 78400*13.5 = 1058400 J

To find the weight of water, begin by way of finding the density(1 kg/L at 39.2°) and the extent of water. Convert the volume of water to liters after which multiply by way of the density to discover the burden.

Density is useful in calculating the load of materials which can be tough to weigh. you may decide its weight without a doubt with the aid of multiplying the density by using the dimensions, or quantity, of the item.

The unique weight, additionally called the unit weight, is the weight in keeping with the unit quantity of cloth. A typically used value is the precise weight of water in the world at 4 °C (39 °F), which is nine.807 kilonewtons consistent with cubic meters or 62. 43 pounds-force in keeping with cubic foot.

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Answer:

D. A followed by B

Explanation:

You can see at section A solid Ice at temperature 0°C gets heated up for and all the energy generated from heating up the ice is used to break the bonds which holds the ice together as a solid .

while at Section B the liquid water at 100°C changes to vapor because the heat energy applied here breaks intermolecular bonds c.

The section where A is followed by C of the heating curve illustrate this process. The correct option is D.

The heating curve represents the association between the supply temperature of the heating system and the external air temperature.

As can be seen in section A reliable Ice at 0°C is heated, and all of the energy generated by heating the ice is used to shatter the bonds that hold the ice together as a solid.

While in Section B, liquid water at 100°C transforms to vapor because the heat energy applied here shatters the intermolecular bonds c.

Thus, the correct option is D.

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22 year solar cycle is characterized by a variation in the number of sunspots and a reversal of the polarity of the Sun as a whole.

What are sunspots?

Sunspots are caused by disturbances in the Sun's magnetic field welling up to the Sun's visible surface.

Sunspot are region of the earth that are more darker than other surfaces. They have a reduced temperature.

If sunspots are active, more solar flares will result creating an increase in geomagnetic storm activity for Earth.

Here, the sun's magnetic field changes polarity approximately every 11 years. So, for reversal polarity of the sun, 22 year solar cycle is characterized by a variation in the number of sunspots and a reversal of the polarity of the Sun as a whole.

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The answer is 24 J

F K =.25*8 N

     = 2N

F = f k = 2 N

Since a = 0

W = f * s

 2 N * 12 m = 24 J

The coefficient of friction is a ratio used to quantify the friction force among two gadgets when it comes to the everyday pressure this is keeping them collectively. The coefficient of friction is critical attention at some stage in material selection and floor requirement determination.

For instance, ice on steel has a low coefficient of friction – the 2 materials slide past each different without problems – whilst rubber on the pavement has an excessive coefficient of friction – the substances no longer slide past each other without difficulty.

The coefficient of friction is dimensionless and it does not have any unit. it is a scalar, meaning the direction of the force does not have an effect on the physical quantity. The coefficient of friction depends on the gadgets that are causing friction.

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(1) The wavelength of the wave is 1.57 m.

(2) The velocity of the wave is 30 m/s .

(3) The frequency of the wave is 19.10 Hz and the time period of the    wave is 0.052 s.

Note: The given equation seems to be incomplete. Most probably the equation was y=25sin(120t-4x). And the standard system of units (i.e. kg, m, s) is used.

Wavelength: The distance between the consecutive crest or trough of a wave is called the wavelength of a wave.

The equation of a plane wave oscillating in the y direction and traveling in the x direction is given by the equation,

y=A sin(ωt-kx)

where y is the displacement along the y direction, A is the amplitude of the wave, ω is the angular frequency, t is the time, x is the displacement along the x direction, and k is the wave constant.

The given equation is,

y=25sin(120t-4x)

Comparing this equation with the above equation, following values are obtained.

k= 4 m^(-1)

ω =120 rad/s

A=25

The wavelength λ is given by the formula,

λ=2π/k

Here k = 4 m^(-1), so

λ=2π/4

λ=1.57 m.

Velocity: The velocity of a wave is the product of the frequency and the wavelength.

The velocity v is given by the formula,

v=ω*λ/2π

Here ω=120 rad/s and λ=1.57 m, so

v=120*1.57/2π

v=30 m/s

Frequency: The number of oscillations completed in one second is called the frequency of a wave.

The formula of the frequency is,

f=v/λ

Here v=30 m/s and λ=1.57 m, so

f=30/1.57

f=19.10 Hz

Time period: The time taken to complete one cycle of oscillation is called the time period of oscillation.

The formula to calculate the time period T is,

T=2π/ω

Here ω=120 rad/s, so

T=2π/120

T=0.052 s.

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