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DaniilM [7]
3 years ago
7

Dimension of radius of sphere​

Physics
1 answer:
Readme [11.4K]3 years ago
5 0

Answer:

The dimension is L

Explanation:

Dimension analysis is a method of representing quantities majorly with respect to some fundamental quantities of mass (M), length (L), time (T).

A sphere has a definite volume which relates to its radius by:

V = \frac{4}{3}\pir^{3}

In this equation \pi is a dimensionless quantity, and the unit of v is m^{3}.

But, metre is a measure of length, thus it has a dimension of L.

So that,

m^{3} ≅ L^{3}

Then,

L^{3} = r^{3}

Find the cube root of both sides to have,

r = L

Therefore, the dimension of the radius of a sphere is L.

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A vertical spring has a mass hanging from it, which is displaced from the equilibrium position and begins to oscillate. At what
Orlov [11]

Answer:

the object has least potential energy at mean position of the SHM

Explanation:

If a block is connected with a spring and there is no resistive force on the system

In this case the total energy of the system is always conserved and it will change from one form to another form

So here we will say that

Kinetic energy + Potential energy = Total Mechanical energy

As we can say that total energy is conserved so here we have least potential energy when the system has maximum kinetic energy

So here we also know that at mean position of the SHM the system has maximum speed and hence maximum kinetic energy.

So the object has least potential energy at mean position of the SHM

5 0
3 years ago
Two particles oscillate in simple harmonic motion along a common straight-line segment of length 1.0 m. Each particle has a peri
igor_vitrenko [27]

Answer:

a) the particles are <em>0.217 m </em>apart

b) <em>the particles are moving in the same direction</em>.

Explanation:

a) The amplitude of the oscillations is A/2 and the period of each particle is

T = 1.5 s however, they differ by a phase of π/6 rad. Let the phase of the first particle be zero so that the phase of the second particle is π/6. So we can write the coordinates of each of the particles as,

x₁ = A/2 cos(ωt)

x₂ = A/2 cos(ωt + π/6)

we can write the angular frequency ω, as

ω = 2π / T

so,

x₁ = A/2 cos(2π / T)

x₂ = A/2 cos(2π / T + π/6)

Thus, the coordinates of the particles at t = 0.45 s are,

x₁ = A/2 cos((2π × 0.45) / 1.5)) = -0.155 A

x₂ = A/2 cos((2π × 0.45) / 1.5) + π/6) = -0.372 A

Their separation at that time is, therefore,

Δx = x₁ - x₂

    = -0.155 A + 0.372 A

    = 0.217 A

since A = 1 m

Thus,

<em>Δx  = 0.217 m</em>

<em></em>

<em></em>

b) In order to find their directions, we must take the derivatives at t = 0.45 s.

Therefore,

v₁ = dx₁ / dt

   = (-πA / T) sin(2πt / T)

   = -(π(1) / 1.5) sin(2π(0.45) / 1.5)

   = -1.99

and,

v₂ = dx₂ / dt

   = (-πA / T) sin((2πt / T) + π/6)

   = -(π(1) / 1.5) sin((2π(0.45) / 1.5) + π/6)

   = -1.40

Since both v₁ and v₂ are negative, this shows that <em>the particles are moving in the same direction</em>.

6 0
3 years ago
Time Intervals in Ice Ages
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It started off with 68% less than it did at the peak, and later created a void and melted the remainder of the ice at about 92%
8 0
3 years ago
Can someone help me with these questions please. I will mark brainliest
VladimirAG [237]

Answer:

3: I can´t see the text/image, but it depend on the mass and the force applied to the ball, if both are too high, it will be harder to make a home run. (Second law)

4:It would be easier to make a home run because there is no interruption between the ball and the space the same travels. (Third law)

Explanation:

3 0
3 years ago
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!<br><br> Joules could be used to measure
lyudmila [28]

All of the above, work is a measurement of energy transfer, in Joules.

Potential energy = Joules

Kinetic energy = Joules

The key thing here is that anything having to do with just energy or energy transfer is measured in joules.

4 0
3 years ago
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