Answer:
ρ₀ = 3λ/(2πR⁴)
Explanation:
If we take an elemental part of the cross sectional Area of the infinitely long cylinder.
The small elemental part has a small length dr in the cylinder's radial direction such that the cross sectional Area of the elemental part = 2πr dr
The linear density over the entire radial length of the cylinder will be equal to the sum of (volume charge density × elemental cross sectional Area)
That is,
λ = Σ ρ₀rR × 2πr dr
summing from 0 to R
λ = ∫ᴿ₀ (ρ₀rR × 2πr) dr
λ = ∫ᴿ₀ ρ₀R × 2πr² dr
λ = [ρ₀R × 2πr³/3 ]ᴿ₀
λ = (2π ρ₀R/3) [ r³ ]ᴿ₀
λ = (2π ρ₀R/3) [ R³ ]
λ = 2π ρ₀R⁴/3
ρ₀ = 3λ/(2πR⁴)
Answer:
Final speed of the rocket,
Explanation:
It is given that,
Impulse delivered by an engine, J = 3.5 kg-m/s
Mass of the rocket, m = 120 g = 0.12 kg
To find,
The final speed of the rocket
Solution,
We know that the impulse is equal to the product of mass and velocity o it is equivalent to the change in momentum of an object.
So, the final speed of the rocket once the engine has fired is 29.16 m/s.
The student does zero work on the backpack because the upward force applied by the student is acting <em>perpendicular</em> to the backpack's displacement parallel to the ground.
Answer:
Explanation:
a ) 12.0 lbs - mass
b ) .34 g - mass
c ) 120 kg - mass
As lbs , g and kg are units of mass , these things represent mass . lbs is FPS unit of mass and kg is SI unit . g is CGS unit of force .
d ) 1600 kN It represents force because kN or kilonewton is unit of force .
e ) it represents , length or distance because m or metre is unit of length .
f ) 411 cm It represents length or distance because cm is smaller unit of length
g ) 899 MN or million newton . Like d ) It also represents force . Million newton is higher unit of force .