If you can build a cyclotron with twice the radius, by what factor would the allowed maximum particle energy increase? assume that the magnetic field remains the same.
a. 2
b. 4
c. 8
d. 16

b.4

Explanation:

Let

Magnetic field produced=B

Charge on particle=q

Mass of charged particle=m

Radius=2r

We have to find the k.E of the particle   by what factor increases when radius taken twice .

Maximum K.E of particle in cyclotron=

Substitute radius= 2r

Then, maximum kinetic energy of particle =

Hence, the maximum kinetic energy of the particle increases by 4 when radius taken twice.

b.4

hypothesising or postulating

d₁ = displacement of tern from arctic to antarctic = 11000 miles

d₂ = displacement of tern from antarctic to arctic =   - 11000 miles

d = total displacement for the journey

total displacement for the journey is given as

d = d₁ + d₂

d = 11000 + (-11000)

d = 0 miles

t₁ = time of travel from arctic to antarctic = 3 months = 3 x 30 days = 90 days

t₂ = time of travel from antarctic to arctic = 3 months = 3 x 30 days = 90 days

t = total time of travel

total time of travel is given as

t = t₁ + t₂

t = 90 + 90

t = 180 days

average velocity is given as

average velocity = total displacement/ total time

v = d/t

v = 0/180

v = 0 miles/day