Chapter 9 Special Theory of relativity

Example 9.1 Page no 329

In [2]:
#Given
d=11.5                     #m
w=5*10**-7
v=3*10**4                      #m/s
c=3*10**8

#Calculation
a=2*d*v**2/(w*c**2)

#Result
print"Fringe shift is",a,"Fringes"

Fringe shift is 0.46 Fringes

Example 9.4 Page no 331

In [11]:
#Given
l=6371
v=30*10**3
c=3.0*10**8

#Calculation
A=0.5*2*l*(v/c)**2

#Result
print"Change in length in the diameter is",round(A*10**5,2),"*10**2 m"

Change in length in the diameter is 6.37 *10**2 m

Example 9.5 Page no 331

In [17]:
#Given
a=60.0

#Calculation
v=(a**2+1)*(a**2-1)/a**4

#Result
print"Maximum speed is",v,"c"

Maximum speed is 0.99999992284 c

Example 9.6 Page no 332

In [31]:
#Given
c=3*10**8
a=0.95
b=20

#Calculation
import math
t=b*c/(a*c)
L=math.sqrt(1-a**2)*b
T=L/a

#Result
print"(a) time taken to cover the distance of star from earth", round(t,2),"Years"
print"(b) Time taken is",round(T,2),"Years"

(a) time taken to cover the distance of star from earth 21.05 Years
(b) Time taken is 6.57 Years

Example 9.7 Page no 332

In [36]:
#Given
L=5                           #m
v=0.6
c=1
t=10                          #Second

#Calculation
import math
L0=L/math.sqrt(1-(v/c)**2)
T=t*math.sqrt(1-(v/c)**2)

#Result
print"(a) Length is", L0,"m"
print"(b) Time is",T,"Seconds"

(a) Length is 6.25 m
(b) Time is 8.0 Seconds

Example 9.8 Page no 332

In [40]:
#Given
L0=120
v=0.95                         #C

#Calculation
import math
L=L0*math.sqrt(1-v**2)
t=L/v
T=2*t

#Result
print"Time taken is",round(T,2),"Years"

Time taken is 78.88 Years

Example 9.10 Page no 333

In [44]:
#Given
t=24*60
v=1440
c=1442.0

#Calculation
import math
v=math.sqrt(1-(v/c)**2)

#Result
print"Speed is",round(v,4),"C"

Speed is 0.0526 C

Example 9.11 Page no 333

In [22]:
#Given
B=1.5                            #T
v=0.5                           #c
m0=6.1*10**-31                     #Kg
c=3.0*10**8
e=1.602*10**-19

#Calculation
import math
A=1-(v**2/c**2)
r=(m0*v*c)/(B*math.sqrt(A))

#Result
print"Radius of curvature of path is", r*10**23,"*10**-4 m"

Radius of curvature of path is 6.1 *10**-4 m

Example 9.12 Page no 333

In [63]:
#Given
m=8.0
c=3*10**8                          #m/s
v=1

#Calculation
import math
v=math.sqrt((v-(v/m)**2)*c**2)

#Result
print"Speed of particle is", round(v*10**-8,3),"*10**8 m/s"

Speed of particle is 2.976 *10**8 m/s

Example 9.13 Page no 334

In [68]:
#Given
d=1.5*10**11
a=1.35*10**3
c=3.0*10**8

#Calculation
import math
E=4*math.pi*d**2*a
m=E/c**2

#Result
print"Decrease in the mass of sun per second is",round(m*10**-9,1),"*10**9 Kg"

Decrease in the mass of sun per second is 4.2 *10**9 Kg

Example 9.14 Page no 334

In [73]:
#Given
v=0.8                          #c
m0=2.5*10**-28
c=1
C=3*10**8
V=2.4*10**8

#Calculation
import math
m=m0/(math.sqrt(1-(v/c)**2))
T=(m-m0)*C**2
T1=m0*V**2/2.0

#Result
print "Kinetic energy is",T1,"J"

Kinetic energy is 7.2e-12 J

Example 9.15 Page no 334

In [89]:
#Given
E=3.2*10**-13                   #J
c=3.0*10**8
m0=9.1*10**-31

#Calculation
m=E/c**2
v=(1-(m0/m)**2)

#Result
print"Mass is", round(m*10**30,2)*10**-30,"Kg"
print"Speed is",round(v,3),"C"

Mass is 3.56e-30 Kg
Speed is 0.934 C

Example 9.16 Page no 335

In [91]:
#Given
KE=2.5                         #Mev
m=0.511 

#Calculation
E=KE+m

#Result
print"Total energy is",E,"Mev"

Total energy is 3.011 Mev

Example 9.17 Page no 335

In [105]:
#Given
v=2.0
c=3.8*10**8

#Calculation
import math
V=math.sqrt(1-(1/v)**2)

#Result
print"Speed of particle is", round(V,3),"c"

Speed of particle is 0.866 c

Example 9.18 Page no 335

In [110]:
#Given
e=13.6*1.6*10**-19                       #J
c=3*10**8

#Calculation
m=e/c**2

#Result
print"Loss of mass is",round(m*10**35,2)*10**-35,"Kg"

Loss of mass is 2.42e-35 Kg

Example 9.19 Page no 335

In [116]:
#Given
E=8*10**-11                          #J
c=3.0*10**8

#Calculation
m=E/c**2

#Result
print"Mass of proton is", round(m*10**28,2)*10**-23,"Kg"

Mass of proton is 8.89e-23 Kg

Example 9.20 Page no 336

In [131]:
#Given
m0=2.5*10**-28
c=9*10**16
v=1.5*10**8
c=3.0*10**8
e=1.16*10**-13

#Calculation
import math
X=math.sqrt(1-(v/c))
T=(m0*c*((1/X)-1))/e

#Result
print"Kinetic energy is",round(T*10**8,0),"Mev"

Kinetic energy is 27.0 Mev

Example 9.21 Page no 336

In [143]:
#Given
m=9.1*10**-31                         #Kg
c=3*10**8
e=1.6*10**-19

#Calculation
E=(m*c**2)/e

#Result
print"Energy is",round(E*10**-6,2),"Mev"

Energy is 0.51 Mev

Example 9.22 Page no 336

In [148]:
#given
m0=1.67*10**-27
v=0.8
c=3*10**8
e=1.6*10**-19

#Calculation
import math
E=(m0*c**2/(math.sqrt(1-v**2)))/e

#Result
print"Energy is",round(E*10**-6,0),"Mev"

Energy is 1566.0 Mev

Example 9.23 Page no 337

In [158]:
#Given
v=2.983*10**8                     #m/s
m0=9.101*10**-31
v=100
c=101.0
C=2.998*10**8

#Calculation
import math
V=math.sqrt(v/c)
V1=V*C
m=m0/(math.sqrt(1-(v/c)))
E=m*C**2

#Result
print"Energy is",E
print"Velocity is", round(V1*10**-8,3),"*10**8 m/s"

Energy is 8.2207806109e-13
Velocity is 2.983 *10**8 m/s

Example 9.24 Page no 337

In [161]:
#Given
m0=5*10**-6                     #Kg
C=2.998*10**8

#Calculation
E=m0*C

#Result
print"Energy is",E*10**-2,"*10**2 Joules"

Energy is 14.99 *10**2 Joules

Example 9.25 Page no 337

In [166]:
#Given
m=1.67*10**-27                      #Kg
c=3*10**8
e=1.6*10**-19

#Calculation
E=m*c**2/e

#Result
print"Energy is",round(E*10**-6,0),"Mev"

Energy is 939.0 Mev