The half life of a π - meson at rest is 1 . 8 × 10 - 8 seconds . What will be its half life when it will travel with the speed of c / 2 ?

Applying time dilation concept, Let T 1 2 be half life when it travels with speed v = c 2 . T 1 2 = t 1 2 1 - v 2 c 2 ⇒ T 1 2 = 1 . 8 × 10 - 8 1 - c 2 2 c 2 ⇒ T 1 2 = 1 . 8 × 10 - 8 1 - 1 4 ⇒ T 1 2 = 2 . 8 × 10 - 8 seconds

Determine the relativistic time, if T o is 7 years and the velocity of the object is 0 . 55 C .

Given: T ∘ = 7 years v = 0 . 55 c The Formula for time dilation is given by, T = T ∘ 1 - v 2 c 2 Where, T is the time observed, T ∘ is the time observed at rest, v is the velocity of the object, c is the velocity of light in a vacuum 3 × 10 8 ms - 2 . T = 7 1 - 0 . 55 2 3 2 × 10 16 3 2 × 10 16 T = 7 1 - 0 . 55 2 , T = 7 0 . 8351 ∴ T = 8 . 38 years

An atomic clock is placed in a jet aeroplane. The clock measures a time interval of 3600 s , when the jet moves with speed 400 m sec . How much larger a time interval does an identical clock held by an observer at rest on the ground measure?

We take the S frame to be attached to the Earth and the S ' frame to be the rest frame of the atomic clock. ∆ t = γ ∆ t ' ∴ γ ≃ 1 + β 2 2 and ∆ t = ∆ t = ∆ t ' ≃ β 2 ∆ t ' 2 It follows that ∆ t = 3 . 2 x 10 - 9 s when v = 400 m / s and t ’ = 3600 s .

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A certain particle called $μ -$ mesons has lifetime of $2 \times 10^{- 6} \sec$ . What is the mean lifetime when the particle is travelling with a speed of $2.944 \times 10^{10} \frac{cm}{\sec}$ . How for it goes during one mean life?

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Important Questions on Relativity

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Physics>Modern Physics>Relativity>Time Dilation

Cotyledons are also called-

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Represent the union of two sets by Venn diagram for each of the following.

$X = {x | x$ is a prime number between $80$ and $100}$

$Y = {y | y$ is an odd number between $90$ and $100}$

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Physics>Modern Physics>Relativity>Time Dilation

The half life of a

π - meson

at rest is

1.8 \times 10^{- 8} seconds .

What will be its half life when it will travel with the speed of

c / 2

EASY

Physics>Modern Physics>Relativity>Time Dilation

A clock keeps correct time on earth. It is put in a space-ship travelling with velocity

\frac{c}{2}

. How many hours does it appear to lose in one day

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Physics>Modern Physics>Relativity>Time Dilation

A person travels by a car at a speed of

180 km / h

. It takes exactly

10 hours

by his wristwatch to go from the station A to the station B. Calculate the difference between time taken in the road frame by the car to go from the station A to the station B and the time measured by wristwatch.

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Physics>Modern Physics>Relativity>Time Dilation

A clock keeps correct time on earth. It is put in a space-ship travelling with velocity

\frac{c}{2}

. If the number of hours it loses in a day are

24 - x \sqrt{3}

. Find

x

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Physics>Modern Physics>Relativity>Time Dilation

The half-life of a

π - meson

at rest is

4.2 \times 10^{- 6} seconds .

Its half-life when it will travel with the speed of

c / 4

is _____

\times 10^{- 6} s

. (Approximate up to two decimal places)

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Physics>Modern Physics>Relativity>Time Dilation

Two babies are born in a moving train, one in the compartment adjacent to the engine and other in the compartment adjacent to the guard. According to the train frame, the babies are born at the same instant of time. Who is elder according to the ground frame ?

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Physics>Modern Physics>Relativity>Time Dilation

What is the dilation factor of a muon travelling with a velocity of

80 %

that of the velocity of light?

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Physics>Modern Physics>Relativity>Time Dilation

A certain particle called

π =

mesons is travelling with a speed of

60 %

of the velocity of light. If it has a lifetime of

4 \times 10^{- 6} \sec

. How for it goes during one mean life?

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Physics>Modern Physics>Relativity>Time Dilation

Suppose a cosmic ray colliding with a nucleus in the Earth’s upper atmosphere produces a muon that has a velocity

v = 0.950 c

. The muon then travels at constant velocity and lives

1.52 μs

as measured in the muon’s frame of reference. (You can imagine this as the muon’s internal clock.) How long does the muon live as measured by an Earth-bound observer?

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Physics>Modern Physics>Relativity>Time Dilation

A frame of reference has four coordinates

x, y, z

and

t

is referred to as the________.

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Physics>Modern Physics>Relativity>Time Dilation

Amount of by which measured time interval is greater than corresponding proper time interval is called:

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Physics>Modern Physics>Relativity>Time Dilation

A particle is travelling through the Earth's at morpheme at a speed of

0.866 C

. To an earth-bound observer, the distance. It travels

2.50 km

. How for does the particle travel in the particle frame of reference?

EASY

Physics>Modern Physics>Relativity>Time Dilation

Determine the relativistic time, if

T_{o}

7

years and the velocity of the object is

0.55 C

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Physics>Modern Physics>Relativity>Time Dilation

An atomic clock is placed in a jet aeroplane. The clock measures a time interval of

3600 s

, when the jet moves with speed

400 \frac{m}{\sec}

. How much larger a time interval does an identical clock held by an observer at rest on the ground measure?

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Physics>Modern Physics>Relativity>Time Dilation

What is time dilation?

A certain particle called μ-mesons has lifetime of 2×10-6sec. What is the mean lifetime when the particle is travelling with a speed of 2.944×1010 cmsec. How for it goes during one mean life?

Important Questions on Relativity

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A certain particle called $μ -$ mesons has lifetime of $2 \times 10^{- 6} \sec$ . What is the mean lifetime when the particle is travelling with a speed of $2.944 \times 10^{10} \frac{cm}{\sec}$ . How for it goes during one mean life?