Advertisements
Advertisements
प्रश्न
If the speed of a particle moving at a relativistic speed is doubled, its linear momentum will _____________ .
पर्याय
become double
become more than double
remain equal
become less than double
Advertisements
उत्तर
become more than double
If a particle is moving at a relativistic speed v, its linear momentum (p) is given as,
\[p = \frac{m_o v}{\sqrt{1 - \frac{v^2}{c^2}}}\]
\[ \Rightarrow p = m_o v \left( 1 - \frac{v^2}{c^2} \right)^\frac{- 1}{2} \]
Expanding binomially and neglecting higher terms we have,
\[p \simeq m_o v\left( 1 + \frac{v^2}{2 c^2} \right)\]
\[ \Rightarrow p \simeq m_o v + \frac{m_o v^3}{2 c^2}\]
If the speed is doubled, such that it is travelling with speed 2v ,linear momentum will be given as
\[p' = \frac{m_o (2v)}{\sqrt{1 - \frac{4 v^2}{c^2}}}\]
\[ \Rightarrow p' = 2 m_o v \left( 1 - \frac{4 v^2}{c^2} \right)^\frac{- 1}{2} \]
Expanding binomially and neglecting higher terms we have,
\[p' \simeq 2 m_o v\left( 1 + \frac{4 v^2}{2 c^2} \right) \]
\[ \Rightarrow p' \simeq 2 m_o v + \frac{4 m_o v^3}{c^2}\]
\[ \therefore p' \simeq 2p + \frac{3 m_o v^3}{c^2}, \frac{3 m_o v^3}{c^2} > 0\]
Therefore, p' is more than double of p.
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?
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.
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.
A 100 W bulb together with its power supply is suspended from a sensitive balance. Find the change in the mass recorded after the bulb remains on for 1 year.
The energy from the sun reaches just outside the earth's atmosphere at a rate of 1400 W m−2. The distance between the sun and the earth is 1.5 × 1011 m.
(a) Calculate the rate which the sun is losing its mass.
(b) How long will the sun last assuming a constant decay at this rate? The present mass of the sun is 2 × 1030 kg.
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?
