Answer:
(a)If two objects collide and one is initially at rest, is it possible for both to be at rest after the collision?
No. Because if you have initial momentum P⃗ ≠0 , if both of the objects were at rest after the collision the total momentum of the system would be P⃗ =0 , which violates conservation of momentum
(b)Is it possible for only one to be at rest after the collision?
Yes, that is perfectly possible. It characteristically, happens when both objects are of the same mass. When two objects of the same mass collide and Kinetic energy is conserved (Perfectly Elastic collision) then the two objects interchange velocities.
Answer:

Explanation:
The radius of the circumference described by a particle in a cyclotron is given by:

m is the particle's mass, v is the speed of the particle, q is the particle's charge and B is the magnitude of the magnetic field.
Kinetic energy is defined as:

Solving this for mv:

Replacing (2) in (1):

For protons, we have:

For alpha particles, we have:

Dividing (4) in (3):

The work done by a gas during an isothermal process is given by:

(1)
where
n is the number of moles of the gas
R is the gas constant
T is the absolute temperature of the gas

is the ratio between the final volume and the initial volume of the gas
We need to calculate this ratio, and we can do it by using the gas pressure. In fact, for an isothermal process, Boyle's law states that the product between pressure and volume of the gas is constant:

which can be rewritten as

which is equivalent to

The problem says that the pressure of the gas is tripled, therefore the ratio between final and initial volume is:

Now we can use eq.(1) to calculate the work done by the gas. The absolute temperature is

The number of moles is n=2, therefore the work done is

And the work is negative, because it is done by the environment on the gas (the gas is compressed)
Answer:
Δx = 2.5 x 10⁻³ m = 2.5 mm
Explanation:
The distance between two consecutive fringes, also known as fringe spacing, in Young's Double Slit Experiment, is given as follows:
Δx = λL/d
where,
Δx = distance between consecutive fringes = ?
λ = wavelength of light = 500 nm = 5 x 10⁻⁷ m
L = Distance between slits and screen = 5 m
d = slit separation = 1 mm = 1 x 10⁻³ m
Therefore,
Δx = (5 x 10⁻⁷ m)(5 m)/(1 x 10⁻³ m)
<u>Δx = 2.5 x 10⁻³ m = 2.5 mm</u>