Which statement best describes the geocentric theory?

A)The Earth and planets revolve around the sun.
B)The stars form concentric spheres around the sun.
C)All celestial bodies revolve around the Earth.

Answer:

D) The force multiplied by the time the objects are in contact

Explanation:

The impulse is defined as the change in momentum of an object:

[tex]I=\Delta p[/tex]

We know that momentum is the product between mas (m) and velocity (v), so assuming the mass of the ball to be constant, its change in momentum will be the product between the mass and the change in velocity:

[tex]I=\Delta p=m\Delta v[/tex]

Now we can multiple and divide by [tex]\Delta t[/tex], the time of collision:

[tex]I=m\Delta v \frac{\Delta t}{\Delta t}=m \frac{\Delta v}{\Delta t}\Delta t[/tex]

But [tex]\frac{\Delta v}{\Delta t}[/tex] is the acceleration, so:

[tex]I=m a \Delta t[/tex]

And (ma) is the force, so we have

[tex]I=(ma)\Delta t=F\Delta t[/tex]

The new period of the object's motion will increase by a factor of √2 of the initial period.

Centripetal acceleration, is the acceleration of a body traversing a circular path.

Mathematically, it is given as

a = v²/r

ar = v²

where;

v = 2πr/T

Substitute the value of v into the above equation;

ar = (2πr/T)²

ar = 4π²r²/T²

a =  4π²r/T²

from the equation above;

a₁T₁² = a₂T₂²

when the acceleration is reduced by half;

a₁T₁² = (0.5a₁)T₂²

T₁² = (0.5)T₂²

2T₁² = T₂²

T₂ = T₁√2

Thus, the new period of the object's motion will increase by a factor of √2 of the initial period.

Learn more about period of circular motion here: https://brainly.com/question/20481765

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Final answer:

To halve the object's acceleration in uniform circular motion without changing the radius, the period must be multiplied by the square root of two. The closest option from the provided choices that would reduce the acceleration is doubling the period, which is option (2) 2T.

Explanation:

The acceleration a of an object in uniform circular motion can be calculated using the formula a = | v |²/r, where v is the velocity of the object and r is the radius of the circle. Alternatively, it can be calculated as a = 4π²r/T², with T being the period of the motion. In order to cut the acceleration in half, either the velocity needs to change or the period has to change since the radius R remains the same.

Given that only the period T can be altered, and based on the second formula for acceleration where the period is squared, if we want to cut the acceleration in half we need to increase the period by a factor that, when squared, equals two.

The square root of two is approximately equal to 1.414, so we need the new period to be T' = T × √2. Since none of the options directly match this value, we can't select an exact answer from the given choices (1) t/2, (2) 2t, (3) t/4, (4) 4t. However, the closest answer that would reduce the acceleration is doubling the period, which is option (2) 2T.