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Stels [109]
3 years ago
7

Two spherical asteroids have the same radius R. Asteroid 1 hasmass M and asteroid 2 has mas 2M. The two asteroids are releasedfr

om rest with distance 10R between their centers. What is thespeed of each asteroid just before they collide?
Physics
1 answer:
gtnhenbr [62]3 years ago
6 0

Answer:

 v_1 =\sqrt{\dfrac{16GM}{15R}}

 v_2 =\sqrt{\dfrac{4GM}{15R}}

Explanation:

given,

mass of asteroid 1 = M

mass of asteroid 2 = 2M

radius of two asteroid = R

Distance between the asteroid = 10 R

Speed of the asteroid before collision = ?

using conservation of momentum

M u + 2M u' = M v₁ + 2 M v₂

initial speed of asteroid is equal to zero

0 = v₁ + 2 v₂

v₁ = -2 v₂

using conservation of momentum

initial potential energy is converted into potential energy and the kinetic energy of both the asteroids.

 \dfrac{GM(2M)}{10R}=\dfrac{GM(2M)}{2R}+\dfrac{1}{2}Mv_1^2 + \dfrac{1}{2}(2M)v_2^2

 \dfrac{GM(2M)}{10R}-\dfrac{GM(2M)}{2R}=\dfrac{1}{2}M(-2v_2)^2 + \dfrac{1}{2}(2M)v_2^2

 6v_2^2 = \dfrac{8GM}{5R}

 v_2 =\sqrt{\dfrac{4GM}{15R}}

now,

 v_1 =-2\sqrt{\dfrac{4GM}{15R}}

 v_1 =\sqrt{\dfrac{16GM}{15R}}

hence, the velocity of asteroid are

 v_1 =\sqrt{\dfrac{16GM}{15R}}

 v_2 =\sqrt{\dfrac{4GM}{15R}}

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3 years ago
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Consider a monochromatic electromagnetic plane wave propagating in the x direction. At a particular point in space, the magnitud
weqwewe [10]

Answer:

a)   S = 2.35 10³   J/m²2 ,  

b)and the tape recorder must be in the positive Z-axis direction.

the answer is 5

c) the direction of the positive x axis

Explanation:

a) The Poynting vector or intensity of an electromagnetic wave is

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if we use that the fields are in phase

          B = E / c

we substitute

         S = E² /μ₀ c

let's calculate

        s = 941 2 / (4π 10⁻⁷  3 10⁸)

        S = 2.35 10³   J/m²2

 

b) the two fields are perpendicular to each other and in the direction of propagation of the radiation

In this case, the electro field is in the y direction and the wave propagates in the ax direction, so the magnetic cap must be in the y-axis direction, and the tape recorder must be in the positive Z-axis direction.

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Answer:

The possible thickness of the soap bubble = 1.034\times 10^{-7}\ m.

Explanation:

<u>Given:</u>

  • Refractive index of the soap bubble, \mu=1.33.
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Let the thickness of the soap bubble be t.

It is given that the soap bubble appears very bright, it means, there is a constructive interference takes place.

For the constructive interference of light through a thin film ( soap bubble), the condition of constructive interference is given as:

2\mu t=\left ( m+\dfrac 12 \right )\lambda.

where m is the order of constructive interference.

Since the soap bubble is appearing very bright, the order should be 0, as 0^{th} order interference has maximum intensity.

Thus,

2\mu t=\left (0+\dfrac 12\right )\lambda\\t=\dfrac{\lambda}{4\mu}\\\ \ = \dfrac{550\times 10^{-9}}{4\times 1.33}\\\ \ = 1.034\times 10^{-7}\ m.

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