Question

the muzzle velocity of a rifle bullet is 900 m/s if the rifle bullet weighs 30g with what accuracy can the position of the bullet be measured without perturbing the momentum by more than 1 part in million?

Answer 1

Using uncertanity principle;

dp*dx>=h/(4*pi)

where h is plank constant

&

h=6.626*10^-34

since,

p=mv=30*10^-3*900=27

&

dp=27/10^6=2.7*10^-5

hence

dx=1.95289*10^-30 m

Answer 2

Applying Heisenberg"s uncertainity principle

X * P = h/2 pi

where P is the uncertainity in momemtum of the bullet ,

X is the uncertainity in the position

X * 10^6 = 6.625 * 10^-34 /6.14

X= 6.625 * 10^-34/6.14* 10^6

X=1.08 * 10^-40 m

Answer 3

Heisenberg's Uncertainty Principle Delta(x)*Delta(p)=h/(4*pi) (x is position, p momentum)

so Delta(p)= 1*10^-6 (parts per million)

delta(x) = h*10^6/(4*pi)

= 5.27*10^-29 m