Physics, 19.11.2019 00:31 nhester3378

How would the speed of earth's orbit around the sun change if earth's distance from the sun
increased by 4 times?
1. it would increase by a factor of 2.

2. it would increase by a factor of 4.

3. it would decrease by a factor of 2.

4. the speed would not change.

Answers: 1

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Answers

If Earth’s distance from the sun increased by 4 times then the speed of Earth’s orbit around the sun would decrease by a factor of 2.

Option 3

Explanation:

From Newton’s second law of motion, it is known that any kind of external force acting on an object will be equal to object’s mass and acceleration exerted on the object. So in this case, the gravitational force between Earth and Sun will be equal to the mass (M) and acceleration exerted on Earth.

$\text {Gravitational force}=\text {M} \times \text {Acceleration of Earth around the orbit}$

It is known that,

$\text {Acceleration in orbital motion}=\frac{\left(\text {velocity at which the Earth rotates)}^{2}\right.}{\text { Distance of Earth from the Sun}}$

Thus, substituting this, we get,

$\text {Gravitational force}=\frac{\text {M} \times\left(\text {velocity at which the Earth rotates)}^{2}\right.}{\text { Distance of Earth from the sun}}$

Also, we know,

$\text {Gravitational force}=\frac{G \times M \text { of sun } \times \text {M of Earth}}{(\text {Distance of Earth from the Sun})^{2}}$

Then, comparing both the equation, we get the orbital velocity as,

$\text { Orbital velocity } v=\sqrt{\frac{G \times M \text { of Sun }}{\text { Distance of Earth from the Sun }}}=\sqrt{\frac{G M}{r}}$

So, here G is gravitational constant, M is the mass of Sun and r is the distance of separation of Earth from Sun.

If the distance of Earth from Sun increases by 4 times so r’ will be 4r. Thus the new orbital velocity v’ will be

$v^{\prime}=\sqrt{\frac{G M}{r^{\prime}}}=\sqrt{\frac{G M}{4 r}}=\frac{1}{2} \sqrt{\frac{G M}{r}}$

So,

$v^{\prime}=\frac{1}{2} v$

Thus, the orbital speed will be decreased by a factor of 2 when the distance of Earth from the Sun increased by 4 times.

Answer from: Quest

i believe it is b. what was the cause of the big bang

hope this !

Answer from: Quest

m₁v₁ + m₂v₂ = (m₁ + m₂)vmomentum is conserved.the left-hand side of the equation represents the momentum in the system before the collision.the right-hand side represents the momentum in the system after the collisionm₁ and v₁ represents the mass and the velocity of the physics blockm₂ and v₂ represents the mass and velocity of the ball of puttyv represents the final velocity of the combined mass.the question states the two masses stick together. they combined mass has its own velocity with the body mass the sum of the two objects' massestheir combined momentum is (m₁ + m₂)vto find the magitude of (m₁ + m₂)v, we need to add the vectors on the left-hand side of the equation: m₁v₁ + m₂v₂.note the diagram. i have positioned the vectors in accordance with their directions.the magnitude of the resultant can be calculated using the pythagorean theorem since this is a right triangle situation (north and west are perpendicular)|(m₁ + m₂)v| = √[ (m₁v₁)² + (m₂v₂)² ]|(m₁ + m₂)v| = √[ (1.5kg·8.0m/s)² + (0.40kg·20m/s)² ]|(m₁ + m₂)v| = 14.4 kg m/sfor two significant figures (assuming that 20m/s is two), this rounds to 14 kg m/s

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