Advertisements
Advertisements
प्रश्न
If the speed of a rod moving at a relativistic speed parallel to its length is doubled,
(a) the length will become half of the original value
(b) the mass will become double of the original value
(c) the length will decrease
(d) the mass will increase
Advertisements
उत्तर
(c) the length will decrease
(d) the mass will increase
If the speed of a rod moving at a relativistic speed v parallel to its length, its mass \[m = \gamma m_o = \frac{m_o}{\sqrt{1 - \frac{v^2}{c^2}}}\]
and its length \[l = \frac{l_o}{\gamma} = l_o \sqrt{1 - \frac{v^2}{c^2}}\]
where \[\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}} = \left( 1 - \frac{v^2}{c^2} \right)^\frac{- 1}{2} = 1 + \frac{v^2}{2 c^2} + . . . > 1\text{ as } v < c\]
If the speed is doubled, its multiplying factor
\[\gamma' = \frac{1}{\sqrt{1 - \frac{4 v^2}{c^2}}} = \left( 1 - \frac{4 v^2}{c^2} \right)^\frac{- 1}{2} = 1 + \frac{2 v^2}{c^2} + . . . > 2\gamma\]
and \[m = \gamma' m_o > 2\gamma m_o , l = \frac{l_o}{\gamma'} < \frac{l_o}{2\gamma}\]
Hence, the mass will increase but more than double and length will decrease but not exactly half of the original values.
APPEARS IN
संबंधित प्रश्न
Mass of a particle depends on its speed. Does the attraction of the earth on the particle also depend on the particle's speed?
If the speed of a particle moving at a relativistic speed is doubled, its linear momentum will _____________ .
Mark the correct statements:-
(a) Equations of special relativity are not applicable for small speeds.
(b) Equations of special relativity are applicable for all speeds.
(c) Nonrelativistic equations give exact result for small speeds.
(d) Nonrelativistic equations never give exact result.
Which of the following quantities related to an electron has a finite upper limit?
A rod of rest length L moves at a relativistic speed. Let L' = L/γ. Its length
(a) must be equal to L'
(b) may be equal to L
(c) may be more than L' but less than L
(d) may be more than L
When a rod moves at a relativistic speed v, its mass ________________ .
By what fraction does the mass of a spring change when it is compressed by 1 cm? The mass of the spring is 200 g at its natural length and the spring constant is 500 N m−1.
Find the increase in mass when 1 kg of water is heated from 0°C to 100°C. Specific heat capacity of water = 4200 J kg−1 K−1.
Find the loss in the mass of 1 mole of an ideal monatomic gas kept in a rigid container as it cools down by 100°C. The gas constant R = 8.3 J K−1 mol−1.
By what fraction does the mass of a boy increase when he starts running at a speed of 12 km h−1?
Find the mass, the kinetic energy and the momentum of an electron moving at 0.8c.
Through what potential difference should an electron be accelerated to give it a speed of (a) 0.6c, (b) 0.9c and (c) 0.99c?
Find the speed of an electron with kinetic energy (a) 1 eV, (b) 10 keV and (c) 10 MeV.
What is the kinetic energy of an electron in electron volts with mass equal to double its rest mass?
Choose the correct answer from given options
The graph showing the correct variation of linear momentum (p) of a charge particle with its de-Broglie wavelength (λ) is _____________.
