Home
Class 12
PHYSICS
Two events A and B occur at places separ...

Two events A and B occur at places separated by `10^(6) km`, B occuring 5s after A . (a) Find the velocity of a frame in which these events occur at the same place . (b)What is the time interval between the events in this frame ?

Text Solution

Verified by Experts


(a) Suppose the events A and B occur at points X and Y at times t_A and t_B where t_B = t_A +5 s. Consider a small train which is at the point X when the event A occurs. Suppose, this same train moves towards Y and reaches the point Y when the events A and B occur at the same place in the train frame . This frame moves `10^(6)` km in 5s as seen from the original frame . Thus, the velocity of the train frame is
` v =10^(6) km / 5 s = 2 xx 10 s m s ^(-1) `
(b) As the events A and B occur at the same place in the train frame, the time interval between the events measured in this frame is the proper interval . Thus , this time interval is ,
`= (5 5) (sqrt 1 - v^(2)/ c^(2) ) = (5s) (sqrt 1 - (2/ 3 )^(2) `
`= 3.7s`
Promotional Banner

Topper's Solved these Questions

  • THE SPECIAL THEORY OF RELATIVITY

    HC VERMA ENGLISH|Exercise Objective|2 Videos

  • THE SPECIAL THEORY OF RELATIVITY

    HC VERMA ENGLISH|Exercise Objective 2|1 Videos

  • THE SPECIAL THEORY OF RELATIVITY

    HC VERMA ENGLISH|Exercise Short answer|2 Videos

  • THE NUCLEOUS

    HC VERMA ENGLISH|Exercise Short answer|12 Videos

  • THERMAL AND CHEMICAL EFFECT OF ELECTRIC CURRENT

    HC VERMA ENGLISH|Exercise Short Question|9 Videos

Similar Questions

Explore conceptually related problems

If A and B are two events, the probability that at most one of these events occurs is

For any two events A and B in a sample space, choose the correct option (s)

Two events A and B are such that P(B) = 0 . 55 and P(AB') = 0 . 15 . The probability of occurence of at least one of event is

Two key events take place, during S-phase in animal cells, DNA replication and duplication of centriole. In which parts of the cell these events occur ?

Name the stage of cell cycle at which one of the following events occur Centromere splits and chromatids separate.

For the three events A , B and C , P (exactly one of the events A or B occurs) = P (exactly one of the events B or C occurs) =P (exactly one of the events C or A occurs) = p and P (all the three events occur simultaneously) = p^2 , where 0ltplt1/2 . Then, find the probability of occurrence of at least one of the events A , B and C .

A train of length l=350m starts moving rectilinearly with constant acceleration w=3.0*10^-2 m//s^2 , t=30s after the start the locomotive headlight is switched on (event 1), and tau=60s after that event the tail signal light is switched on (event 2). Find the distance between these events in the reference frames fixed to be train and to the Earth. How and at what constant velocity V relative to the Earth must a certain reference frame K move for the two events to occur in it at the same point?

A and B are two independent events.The probability that both A and B occur is 1/6 and the probability that neither of them occurs is 1/3.Then the probability of the two events are respectively:

For the three events A ,B , and C , P (exactly one of the events A or B occurs)= P (exactly one of the two evens B or C )= P (exactly one of the events C or A occurs)= p and P (all the three events occur simultaneously)= p^2 where 0 < p < 1//2 . Then the probability of at least one of the three events A , B and C occurring is

Two events A and B have probabilities 0.25 and 0.50 respectively.The probability that both A and B occur simultaneously is 0.1 .Find the probability that neither A nor B occurs .