# Numerical Problem.doc

**Numerical Problem**

**Posted by Shrey Kumar Pandey**

**Theory of Relativity**

Length contraction

Q.1: a rod of 1 m length is mooving along its length with a velocity of 0.6c .calculate its length as it appears on the earth & also observed by an observer moving with the rod?

Q.2: how fast could a rocket have to go related to an observer for its length to be contracted to 99% of its length at rest?

Q.: explain and prove how the circle seems to be contracted to elepthical shape?

Q.: how the linne will cintract if it is moving when it is inclined at an angle with x- axis?

Time dilation

Q.3: the mean lifetime of a neuclear particle is 9x 10-6 sec as measured by an observer at rest relative to particle. The particle is moving with velocity 0.9 c then what is its life time?

Q.4: a clock in a space ship emits signnals at intervals of 1 sec. As observed by an austronout in the space ship.if the space ship travells with a speed of 3x 107 m sec-1.what is the interval between successive signals as seen by an observer in the control tower on earth?

Q.5: a particle with a proper lifetime of 1 micro sec. Moves through the laboratory at 2.7 x 108 m sec-1.what is its life time as measured by observer in the laboratory and the distance travelled by it before it integrate?

Velocity addition

Q.6: an experimentor observes a radioactive atom moving with a velocity of 0.25 c. Then emits α, β particle which have a velocity of 0.9 c relative to the atom in the direction of its motion. What is the velocity of the β particle as observed by the experimentor?

Q.7: an electron is moving with a speed of 0.85 c in a direction opposite to that of a oving photon. Calculate the relative velocity of the photon with respect to the electron?

Variation of mass

Q.8: at what speed is a particle moving if the mass is equal to three times its rest mass?

Mass energy equivalence

Q.9: find energy in 1 amu mass ?

Q.10: calculate the rest energy of electronin jouls and

Q.11: if 4 kg of a substance is fully converted into energy. How much energy it will produce?

Q.12: calculate the kinetic energy of a moving electron with a velocity of 0.98 c in the laboratory?

**Light**

Young’s double slit experiment

Q.1: in young’s double slit experiment a transparent film of μ=1.5 is introduced in the path of one of the beam. If the central fringe get shifted by 0.2 cm. Calculate the thickness of mica sheet. The separation between the two slits is 0.1 cm and distance between screen and slit is 50 cm?

Q.2: for a λ=5.89 x 10-5 , β is 0.431 mm after putting a thin mica sheet of μ=1.59 in the path of one ray. Calculate the thickness of the sheet when the central fringe is shifted by 1.89 mm?

Q.3: in young’s double slit experiment a transparent film of thickness 10-3 cm is introduced in the path of one beam. Central fringe is displaced by 8th bright fringe. Calculate the μ of the fringe? Given λ= 6000 å.

Newton’s ring experiment

Q.4: in newton’s ring experiment sodium light is normally incedent, the diameter of the 10th dark ring is 0.5 cm. Find the radius of curvature of the lens used and the thickness of the air film at the point?

Q.5: in newton’s ring experiment diameter of 3rd and 23rd bright ring is 0.18 cm and 0.501 cm. Calculate λ if the radius of curvature is ½ m?

Q.6: in newton’s ring experiment diameter of 10th dark ring changes from 0.3 cm to 0.25 cm when oil is used. Calculate μ?

Q.7: why the central ring is dark in newton’s ring experiment? Prove it.

Note:

μ=refractive index

λ = wavelength of light

å = 10-10 m