Special Relativity - Classical Mechanics - Physics Previous Year Questions

1

2007 · Physics · Classical Mechanics · Special Relativity

Physics (PH) 2007

The speed of the particle P in the rest frame of the particle Q is

A

\(\frac{7c}{95}\)

B

\(\frac{13c}{85}\)

C

\(\frac{3c}{5}\)

D

\(\frac{63c}{95}\)

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2

2007 · Physics · Classical Mechanics · Special Relativity

Physics (PH) 2007

The energy of the particle P in the rest frame of the particle Q is

A

\(\frac{1}{2}m_0c^2\)

B

\(\frac{5}{4}m_0c^2\)

C

\(\frac{19}{13}m_0c^2\)

D

\(\frac{11}{9}m_0c^2\)

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3

2008 · Physics · Classical Mechanics · Special Relativity

Physics (PH) 2008

The rate of a clock in a spaceship "Suryashakti" is observed from earth to be 3/5 of the rate of the clocks on earth. The speed of the spaceship "Suryashakti" relative to earth is

A

\(\frac{4}{5} c\)

B

\(\frac{3}{5} c\)

C

\(\frac{9}{10} c\)

D

\(\frac{2}{5} c\)

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4

2008 · Physics · Classical Mechanics · Special Relativity

Physics (PH) 2008

The rate of a clock in a spaceship "Aakashganga" is observed from earth to be 5/13 of the rate of the clocks on earth. If both Akashganga and Suryashakti are moving in the same direction relative to someone on earth, then the speed of Akashganga relative to Suryashakti is

A

\(\frac{12}{13} c\)

B

\(\frac{4}{5} c\)

C

\(\frac{8}{17} c\)

D

\(\frac{5}{6} c\)

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5

2009 · Physics · Classical Mechanics · Special Relativity

Physics (PH) 2009

Assuming the mean life time of a muon (in its rest frame) to be 2×10^-6 s, its life time in the laboratory frame, when it is moving with a velocity 0.95c is

A

6.4×10^-6 s

B

0.62×10^-6 s

C

2.16×10^-6 s

D

0.19×10^-6 s

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6

2010 · Physics · Classical Mechanics · Special Relativity

Physics (PH) 2010

For the set of all Lorentz transformations with velocities along the \( x \)-axis, consider the two statements given below:
P: If \( L \) is a Lorentz transformation then, \( L^{-1} \) is also a Lorentz transformation.
Q: If \( L_1 \) and \( L_2 \) are Lorentz transformations, then \( L_1L_2 \) is necessarily a Lorentz transformation.
Choose the correct option.

A

P is true and Q is false.

B

Both P and Q are true.

C

Both P and Q are false.

D

P is false and Q is true.

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7

2010 · Physics · Classical Mechanics · Special Relativity

Physics (PH) 2010

A \( \pi^0 \) meson at rest decays into two photons, which move along the x-axis. They are both detected simultaneously after a time, \( t = 10 \) s. In an inertial frame moving with a velocity \( V = 0.6 c \) in the direction of one of the photons, the time interval between the two detections is

A

15 s

B

0 s

C

10 s

D

20 s

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8

2011 · Physics · Classical Mechanics · Special Relativity

Physics (PH) 2011

Two particles, each of rest mass \( m \) collide head-on and stick together. Before collision, the speed of each mass was 0.6 times the speed of light in free space. The mass of the final entity is

A

\(5m/4 \)

B

\(2m \)

C

\(5m/2 \)

D

\(25m/8 \)

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9

2012 · Physics · Classical Mechanics · Special Relativity

Physics (PH) 2012

A rod of proper length \( l_0 \) oriented parallel to the x-axis moves with speed \( 2c/3 \) along the x-axis in the S-frame, where \( c \) is the speed of the light in free space. The observer is also moving along the x-axis with speed \( c/2 \) with respect to the S-frame. The length of the rod as measured by the observer is

A

0.35 \(l_0 \)

B

0.48 \(l_0 \)

C

0.87 \(l_0 \)

D

0.97 \(l_0 \)

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10

2013 · Physics · Classical Mechanics · Special Relativity

Physics (PH) 2013

An electron is moving with a velocity of \(0.85c\) in the same direction as that of a moving photon. The relative velocity of the electron with respect to photon is

A

\(c\)

B

\(-c\)

C

\(0.15c\)

D

\(-0.15c\)

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11

2013 · Physics · Classical Mechanics · Special Relativity

Physics (PH) 2013

The relativistic form of Newton's second law of motion is

A

F = (mc/√(c^2-v^2)) dv/dt

B

F = (m√(c^2-v^2)/c) dv/dt

C

F = (c^2-v^2)/c^2 dv/dt

D

F = m (c^2-v^2)/c^2 dv/dt

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12

2014 · Physics · Classical Mechanics · Special Relativity

Physics (PH) 2014

Which one of the following quantities is invariant under Lorentz transformation?

A

Charge density

B

Charge

C

Current

D

Electric field

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13

2014 · Physics · Classical Mechanics · Special Relativity

Physics (PH) 2014

If the half-life of an elementary particle moving with speed 0.9c in the laboratory frame is \(5 \times 10^{-5}\) s, then the proper half-life is _____________ \(\times 10^{-5}\) s. (\(c = 3 \times 10^8\) m/s)

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14

2016 · Physics · Classical Mechanics · Special Relativity

Physics (PH) 2016

The kinetic energy of a particle of rest mass \( m_0 \) is equal to its rest mass energy. Its momentum in units of \( m_0 c \), where c is the speed of light in vacuum, is ______. (Give your answer upto two decimal places)

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15

2016 · Physics · Classical Mechanics · Special Relativity

Physics (PH) 2016

In an inertial frame of reference \( S \), an observer finds two events occurring at the same time at coordinates \( x_1 = 0 \) and \( x_2 = d \). A different inertial frame \( S' \) moves with velocity \( v \) with respect to \( S \) along the positive x-axis. An observer in \( S' \) also notices these two events and finds them to occur at times \( t'_1 \) and \( t'_2 \) and at positions \( x'_1 \) and \( x'_2 \), respectively. If \( \Delta t' = t'_2 - t'_1 \), \( \Delta x' = x'_2 - x'_1 \) and \( \gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}} \), which of the following statements is true?

A

\(\Delta t' = 0, \Delta x' = \gamma d \)

B

\(\Delta t' = 0, \Delta x' = d/\gamma \)

C

\(\Delta t' = -\gamma vd/c^2, \Delta x' = \gamma d \)

D

\(\Delta t' = -\gamma vd/c^2, \Delta x' = d/\gamma \)

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16

2017 · Physics · Classical Mechanics · Special Relativity

Physics (PH) 2017

An object travels along the x-direction with velocity $c/2$ in a frame $O$. An observer in a frame $O'$ sees the same object travelling with velocity $c/4$. The relative velocity of $O'$ with respect to $O$ in units of $c$ is ______. (up to two decimal places)

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17

2018 · Physics · Classical Mechanics · Special Relativity

Physics (PH) 2018

A spaceship is travelling with a velocity of $0.7c$ away from a space station. The spaceship ejects a probe with a velocity $0.59c$ opposite to its own velocity. A person in the space station would see the probe moving at a speed $Xc$, where the value of $X$ is ______ (up to three decimal places).

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18

2019 · Physics · Classical Mechanics · Special Relativity

Physics (PH) 2019

Two spaceships A and B, each of the same rest length \(L\), are moving in the same direction with speeds \(\frac{4c}{5}\) and \(\frac{3c}{5}\), respectively, where \(c\) is the speed of light. As measured by B, the time taken by A to completely overtake B [see figure below] in units of \(L/c\) (to the nearest integer) is __________

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19

2019 · Physics · Classical Mechanics · Special Relativity

Physics (PH) 2019

Two events, one on the earth and the other one on the Sun, occur simultaneously in the earth's frame. The time difference between the two events as seen by an observer in a spaceship moving with velocity 0.5c in the earth's frame along the line joining the earth to the Sun is Δt, where c is the speed of light. Given that light travels from the Sun to the earth in 8.3 minutes in the earth's frame, the value of |Δt| in minutes (rounded off to two decimal places) is ______

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20

2021 · Physics · Classical Mechanics · Special Relativity

Physics (PH) 2021

Two observers \(O\) and \(O'\) observe two events \(P\) and \(Q\). The observers have a constant relative speed of \(0.5c\). In the units, where the speed of light, \(c\), is taken as unity, the observer \(O\) obtained the following coordinates:
Event \(P\): \(x = 5, \; y = 3, \; z = 5, \; t = 3\)
Event \(Q\): \(x = 5, \; y = 1, \; z = 3, \; t = 5\)
The length of the space-time interval between these two events, as measured by \(O'\), is \(L\). The value of \(|L|\) (in integer) is_____.

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