Sheet -1: Special theory of relativity
Ex1
What is the length of a meter stick moving parallel to its length when its mass is 3/2 of its rest
mass?
Ex2
The length of a spaceship is measured to be exactly half its actual length. Calculate:
1- The speed of the spaceship.
2- The time dilation corresponding to one second on the spaceship.
Ex3
The mean life of π meson is 2×10-8 s. Calculate the mean life of a meson moving with a
velocity of 0.8c.
Ex4
A particle of a mass 10-24 Kg is moving with a speed of 1.8 ×108 m/s. Calculate its mass
when it is in motion.
Ex5
A particle is moving with a speed of 0.5C. Calculate the ratio of the rest mass and the mass
while in motion.
Ex6
The rest mass of a proton is 2000 times the rest mass of an electron. Calculate the speed at
which the electron should move so that its mass will be equal to the rest mass of the proton.
Ex7
The density of gold is 19.3×103Kg/m3 in a frame S which is at rest. Calculate its density in a
frame S’ moving along the X-axis with speed 0.9c with respect to the frame S.
Ex8
Calculate the speed of an electron so that it has double its res mass.
Ex9
At what speed will an electron move in order to double its relative mass to the rest mass.
Ex10
A particle of a mass 10-24 Kg is moving with a speed of 1.8 ×108 m/s. Calculate its mass
when it is in motion.
Ex11
A particle is moving with a speed of 0.5C. Calculate the ratio of the rest mass and the mass
while in motion.
Ex12
The total electrical energy generated in a country is 7.5×1011kwh, how much mass was
converted into energy.
Ex13
If 1 Kg of a substance is fully converted into energy, how much energy is produced.
Ex14
Calculate the velocity that one atomic mass unit have if it has a kinetic energy equal to twice
the rest mass energy.
Ex15
The rest mass of a proton is 2000 times the rest mass of an electron. Calculate the speed at
which the electron should move so that its mass will be equal to the rest mass of the proton.
Ex16
The total energy of a particle is exactly twice its rest energy. Calculate its speed.
Ex17
Electrons are accelerated upto a kinetic energy of 109eV. Find:
1- The ratio of their mass to the rest mass.
2- The ratio of their velocity to the velocity of light.
3- The ratio of their energy to the rest mass energy.
Ex18
What fraction of the speed of light is the speed of electron whose kinetic energy is 0.5MeV?
Ex19
An electron has a total energy of 2 MeV. Calculate the effective mass of the electron in Kg
and also its speed. Assume the rest mass of electron to be 0.511MeV.
Ex20
What must be the speed of a particle of rest mass ½ MeV/c2 so that its relativistic mass is
1
MeV/c2?
√2