Ans: A quantity cannot have units until it has dimensions. A quantity that has dimensions must have units. Yes a quantity have units but still be dimensionless for example,unit of angle is radian ,but it is a dimensionless quantity. A dimensionless quantity may have unit.
Answer: e. P/2
Explanation:
For ideal gases, we have the relation:
P*V = n*R*T
where:
n = number of mols
R = Gas constant
T = temperature
V = volume
P = pressure.
We know that for sample A, we have n moles, a temperature T and a volume V, then the pressure of this sample will be:
Pa = (n*R*T)/V.
For sample B, we have:
n/2 moles, temperature T/2 and a volume V/2, then the pressure will be:
Pb = (n/2)*R*(T/2)*(2/V) = (n*R*T/V)*(2/4)
and:
(n*R*T/V) = Pa
Then we can replace it and we get:
Pb = (n*R*T/V)*(2/4) = Pa*(2/4) = Pa*(1/2) = Pa/2.
Then the correct option is e.
As the boulder falls off the cliff, the gravitational potential energy that the boulder has is converted into kinetic energy. If you do the calculations, you will see that the kinetic energy the boulder has is equal to the gravitational potential energy it had before it fell off a cliff.
The self-inductance of a solenoid is given by:

where

is the vacuum permeability
N is the number of turns
A is the cross-sectional area of the solenoid
l is the length of the solenoid
For the solenoid in our problem, N=3000, l=70.0 cm=0.70 m and the self-inductance is L=25.0 mH=0.025 H, therefore the cross-sectional area is

And since the area is related to the radius by

The radius of the solenoid is