In [1]:

```
#importing modules
import math
from __future__ import division
#Variable declaration
L_0 = 1; #For simplicity, we assume classical length to be unity(m)
c = 1; #For simplicity assume speed of light to be unity(m/s)
#Calculation
L = (1-1/100)*L_0; #Relativistic length(m)
#Relativistic length contraction gives L = L_0*sqrt(1-v^2/c^2), solving for v
v = math.sqrt(1-(L/L_0)**2)*c; #Speed at which relativistic length is 1 percent of the classical length(m/s)
v = math.ceil(v*10**4)/10**4; #rounding off the value of v to 4 decimals
#Result
print "The speed at which relativistic length is 1 percent of the classical length is",v, "c"
```

In [2]:

```
#importing modules
import math
from __future__ import division
#Variable declaration
c = 1; #For simplicity assume speed of light to be unity(m/s)
delta_t = 5*10**-6; #Mean lifetime of particles as observed in the lab frame(s)
#Calculation
v = 0.9*c; #Speed at which beam of particles travel(m/s)
delta_tau = delta_t*math.sqrt(1-(v/c)**2); #Proper lifetime of particle as per Time Dilation rule(s)
#Result
print "The proper lifetime of particle is",delta_tau, "s"
```

In [4]:

```
#importing modules
import math
from __future__ import division
#Variable declaration
c = 1; #For simplicity assume speed of light to be unity(m/s)
#Calculation
v = 0.6*c; #Speed with which the rocket leaves the earth(m/s)
u_prime = 0.9*c; #Relative speed of second rocket w.r.t. the first rocket(m/s)
u1 = (u_prime+v)/(1+(u_prime*v)/c**2); #Speed of second rocket for same direction of firing as per Velocity Addition Rule(m/s)
u1 = math.ceil(u1*10**4)/10**4; #rounding off the value of u1 to 4 decimals
u2 = (-u_prime+v)/(1-(u_prime*v)/c**2); #Speed of second rocket for opposite direction of firing as per Velocity Addition Rule(m/s)
u2 = math.ceil(u2*10**4)/10**4; #rounding off the value of u2 to 4 decimals
#Result
print "The speed of second rocket for same direction of firing is",u1,"c"
print "The speed of second rocket for opposite direction of firing is",u2,"c"
```

In [5]:

```
#importing modules
import math
from __future__ import division
#Variable declaration
c = 1; #For simplicity assume speed of light to be unity(m/s)
L0 = 1; #For simplicity assume length in spaceship's frame to be unity(m)
tau = 1; #Unit time in the spaceship's frame(s)
#Calculation
L = 1/2*L0; #Length as observed on earth(m)
#Relativistic length contraction gives L = L_0*sqrt(1-v^2/c^2), solving for v
v = math.sqrt(1-(L/L0)**2)*c; #Speed at which length of spaceship is observed as half from the earth frame(m/s)
t = tau/math.sqrt(1-(v/c)**2); #Time dilation of the spaceship's unit time(s)
v = math.ceil(v*10**4)/10**4; #rounding off the value of v to 4 decimals
#Result
print "The speed at which length of spaceship is observed as half from the earth frame is",v, "c"
print "The time dilation of the spaceship unit time is",t,"delta_tau"
```

In [6]:

```
#importing modules
import math
from __future__ import division
#Variable declaration
c = 3*10**8; #Speed of light in vacuum(m/s)
t1 = 2*10**-7; #Time for which first event occurs(s)
t2 = 3*10**-7; #Time for which second event occurs(s)
x1 = 10; #Position at which first event occurs(m)
x2 = 40; #Position at which second event occurs(m)
#Calculation
v = 0.6*c; #Velocity with which S2 frame moves relative to S1 frame(m/s)
L_factor = 1/math.sqrt(1-(v/c)**2); #Lorentz factor
delta_t = L_factor*(t2 - t1)+L_factor*v/c**2*(x1 - x2); #Time difference between the events(s)
delta_x = L_factor*(x2 - x1)-L_factor*v*(t2 - t1); #Distance between the events(m)
#Result
print "The time difference between the events is",delta_t, "s"
print "The distance between the events is",delta_x, "m"
```

In [9]:

```
#importing modules
import math
from __future__ import division
#Variable declaration
c = 3*10**8; #Speed of light in vacuum(m/s)
tau = 2.6*10**-8; #Mean lifetime the particle in its own frame(s)
d = 20; #Distance which the unstable particle travels before decaying(m)
#Calculation
#As t = d/v and also t = tau/sqrt(1-(v/c)^2), so that
#d/v = tau/sqrt(1-(v/c)^2), solving for v
v = math.sqrt(d**2/(tau**2+(d/c)**2)); #Speed of the unstable particle in lab frame(m/s)
v = v/10**8;
v = math.ceil(v*10)/10; #rounding off the value of v to 1 decimal
#Result
print "The speed of the unstable particle in lab frame is",v,"*10**8 m/s"
```

In [13]:

```
#importing modules
import math
from __future__ import division
#Variable declaration
c = 1; #For simplicity assume speed of light to be unity(m/s)
me = 1; #For simplicity assume mass of electron to be unity(kg)
tau = 2.3*10**-6; #Average lifetime of mu-meson in rest frame(s)
t = 6.9*10**-6; #Average lifetime of mu-meson in laboratory frame(s)
e = 1.6*10**-19; #Energy equivalent of 1 eV(J/eV)
C = 3*10**8; #Speed of light in vacuum(m/s)
m_e = 9.1*10**-31; #Mass of an electron(kg)
#Calculation
#Fromm Time Dilation Rule, tau = t*sqrt(1-(v/c)^2), solving for v
v = c*math.sqrt(1-(tau/t)**2); #Speed of mu-meson in the laboratory frame(m/s)
v = math.ceil(v*10**5)/10**5; #rounding off the value of v to 5 decimals
m0 = 207*me; #Rest mass of mu-meson(kg)
m = m0/math.sqrt(1-(v/c)**2); #Relativistic variation of mass with velocity(kg)
m = math.ceil(m*10)/10; #rounding off the value of m to 1 decimal
T = (m*m_e*C**2 - m0*m_e*C**2)/e; #Kinetic energy of mu-meson(eV)
T = T*10**-6; #Kinetic energy of mu-meson(MeV)
T = math.ceil(T*100)/100; #rounding off the value of T to 2 decimals
#Result
print "The speed of mu-meson in the laboratory frame is",v, "c"
print "The effective mass of mu-meson is",m, "me"
print "The kinetic energy of mu-meson is",T, "MeV"
```

In [14]:

```
#importing modules
import math
from __future__ import division
#Variable declaration
c = 1; #For simplicity assume speed of light to be unity(m/s)
m0 = 1; #For simplicity assume rest mass to be unity(kg)
#Calculation
m = (20/100+1)*m0; #Mass in motion(kg)
#As m = m0/sqrt(1-(u/c)^2), solving for u
u = math.sqrt(1-(m0/m)**2)*c; #Speed of moving mass(m/s)
u = math.ceil(u*10**3)/10**3; #rounding off the value of u to 3 decimals
#Result
print "The speed of moving body is",u, "c"
```

In [18]:

```
#importing modules
import math
from __future__ import division
#Variable declaration
c = 3*10**8; #Speed of light in vacuum(m/s)
dE = 4*10**26; #Energy radiated per second my the sun(J/s)
#Calculation
dm = dE/c**2; #Rate of decrease of mass of sun(kg/s)
dm = dm/10**9;
dm = math.ceil(dm*10**3)/10**3; #rounding off the value of dm to 3 decimals
#Result
print "The rate of decrease of mass of sun is",dm,"*10**9 kg/s"
```

In [19]:

```
#importing modules
import math
from __future__ import division
#Variable declaration
c = 1; #For simplicity assume speed of light to be unity(m/s)
m0 = 9.1*10**-31; #Mass of the electron(kg)
E0 = 0.512; #Rest energy of electron(MeV)
T = 10; #Kinetic energy of electron(MeV)
#Calculation
E = T + E0; #Total energy of electron(MeV)
# From Relativistic mass-energy relation E^2 = c^2*p^2 + m0^2*c^4, solving for p
p = math.sqrt(E**2-m0**2*c**4)/c; #Momentum of the electron(MeV)
p = math.ceil(p*100)/100; #rounding off the value of p to 2 decimals
#As E = E0/sqrt(1-(u/c)^2), solving for u
u = math.sqrt(1-(E0/E)**2)*c; #Velocity of the electron(m/s)
u = math.ceil(u*10**4)/10**4; #rounding off the value of u to 4 decimals
#Result
print "The momentum of the electron is",p,"/c MeV"
print "The velocity of the electron is",u, "c"
#answer for velocity given in the book is wrong
```

In [20]:

```
#importing modules
import math
from __future__ import division
#Variable declaration
c = 3*10**8; #Speed of light in vacuum(m/s)
E = 4.5*10**17; #Total energy of object(J)
px = 3.8*10**8; #X-component of momentum(kg-m/s)
py = 3*10**8; #Y-component of momentum(kg-m/s)
pz = 3*10**8; #Z-component of momentum(kg-m/s)
#Calculation
p = math.sqrt(px**2+py**2+pz**2); #Total momentum of the object(kg-m/s)
#From Relativistic mass-energy relation E^2 = c^2*p^2 + m0^2*c^4, solving for m0
m0 = math.sqrt(E**2/c**4 - p**2/c**2); #Rest mass of the body(kg)
m0 = math.ceil(m0*100)/100; #rounding off the value of m0 to 2 decimals
#Result
print "The rest mass of the body is",m0, "kg"
```

In [21]:

```
#importing modules
import math
from __future__ import division
#Variable declaration
c = 3*10**8; #Speed of light in vacuum(m/s)
m = 50000; #Mass of high speed probe(kg)
#Calculation
u = 0.8*c; #Speed of the probe(m/s)
p = m*u/math.sqrt(1-(u/c)**2); #Momentum of the probe(kg-m/s)
#Result
print "The momentum of the high speed probe is",p, "kg-m/s"
```

In [24]:

```
#importing modules
import math
from __future__ import division
#Variable declaration
e = 1.6*10**-19; #Electronic charge, C = Energy equivalent of 1 eV(J/eV)
m0 = 9.11*10**-31; #Rest mass of electron(kg)
c = 3*10**8; #Speed of light in vacuum(m/s)
#Calculation
u1 = 0.98*c; #Inital speed of electron(m/s)
u2 = 0.99*c; #Final speed of electron(m/s)
m1 = m0/math.sqrt(1-(u1/c)**2); #Initial relativistic mass of electron(kg)
m2 = m0/math.sqrt(1-(u2/c)**2); #Final relativistic mass of electron(kg)
dm = m2 - m1; #Change in relativistic mass of the electron(kg)
W = dm*c**2/e; #Work done on the electron to change its velocity(eV)
W = W*10**-6; #Work done on the electron to change its velocity(MeV)
W = math.ceil(W*100)/100; #rounding off the value of W to 2 decimals
#As W = eV, V = accelerating potential, solving for V
V = W*10**6; #Accelerating potential(volt)
V = V/10**6;
#Result
print "The change in relativistic mass of the electron is",dm, "kg"
print "The work done on the electron to change its velocity is",W, "MeV"
print "The accelerating potential is",V, "*10**6 volt"
#answers given in the book are wrong
```

In [ ]:

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