**Answer:**

The final size is approximately equal to the initial size due to a very small relative increase of in its size

**Solution:**

As per the question:

The energy of the proton beam, E = 250 GeV =

Distance covered by photon, d = 1 km = 1000 m

Mass of proton,

The initial size of the wave packet,

Now,

This is relativistic in nature

The rest mass energy associated with the proton is given by:

This energy of proton is

Thus the speed of the proton, v

Now, the time taken to cover 1 km = 1000 m of the distance:

T =

T =

Now, in accordance to the dispersion factor;

Thus the increase in wave packet's width is relatively quite small.

Hence, we can say that:

where

= final width

**Explanation:**

Mass = Weight / g = 150N / (9.8m/s²) = 15.3kg.

Answer:

a.** Big Bang Theory explains the beginning of the universe. The entire matter of the universe is believed to be concentrated in a single point. This point had infinite density. **At time, t = 0, at the big bang, universe started expanding and cooling down. This theory is most widely accepted theory describing the beginning of the universe. It is not considered as hypothesis because of the evidences received by the scientists- detection of cosmic microwave background, red shift of the light received from the galaxies indicating that universe is expanding.

b. **Cosmic Microwave background radiation is a faint radiation having average temperature of 3 K detected every where around from the sky. This is a residual radiation from 400,000 years after the beginning of the universe. **The universe was very hot and dense at the beginning and thus, opaque. Hence, detection of the CMB has provided the evidence of Big bang theory.

c. Scientists have proposed three models of the universe:

1. closed universe- The universe has finite volume and curves around itself. The space-time has positive curvature.

2. open universe - The universe has infinite volume and has a negative curvature.

**3. flat universe - The universe has zero curvature. It has infinite volume. The actual density of the universe is equal to the critical density of the universe. The expansion rate slows down over time. This is the most widely accepted model. **

**13.0m/s**

**1.2m/s**

**Explanation:**

Given parameters:

Initial speed of the body = 7.1m/s

time taken = 2.23s

Acceleration = 2.64m/s²

Unknown:

Final speed = ?

Solution:

Acceleration is the rate of change of velocity with time.

a =

a = acceleration

V = final speed

U = initial speed

T = time taken

Input the variables and solve for V;

2.64 =

V - 7.1 = 5.9 expression 1

V = 5.9 + 7.1 = **13.0m/s**

**B**

**Using the same parameters, the speed after a uniform deceleration of -2.64m/s², the negative sign implies deceleration;**

** from expression 1; **

** V - 7.1 = -5.9**

** V = -5.9 + 7.1 = 1.2m/s**

learn more:

Acceleration brainly.com/question/3820012

#learnwithBrainly

**Answer:**

the most elliptical orbit is that of COMETA

**Explanation:**

The eccentricity of a curve in defined as the ratio between lacia to the focus, called c and the value of the axis greater than

ε = c / a

if we use Pythagoras' theorem

c =

substituting

ε =

if ε = 0 we have a circumference

In the diagram presented the orbit of the comet is an ellipse a> b

ε=

if we expand in series

ε = 1 - x/2

ε=

if we neglect the non-linear terms

ε = 1

Earth's orbit is a small ellipse

b / a = 149 10⁶ / 151 10⁶

b / a = 0.98675

ε =

ε = 0.16

a very small ellipse

Planet X, despite not having data, it seems that the sun is in the scepter of the orbit, so b = a

therefore both the semi-axes of the curve

e = a / b

Consequently, the most elliptical orbit is that of COMETA.