Advertisements
Advertisements
Question
Mass of a particle depends on its speed. Does the attraction of the earth on the particle also depend on the particle's speed?
Advertisements
Solution
Mass of a particle depends on the relativistic speed v with which it moves as
\[m = \frac{m_o}{\sqrt{1 - \frac{v^2}{c^2}}}\]
The gravitational force of attraction of Earth is given by
\[F = \frac{GMm}{r^2}\]
\[ \Rightarrow F = \frac{GM m_o}{r^2 \sqrt{1 - \frac{v^2}{c^2}}}\]
Notes
This is the only reason responsible for gravitational lengthening in which a photon travelling at a speed c experiences gravitational force.
APPEARS IN
RELATED QUESTIONS
The magnitude of linear momentum of a particle moving at a relativistic speed v is proportional to ______________ .
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.
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
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.
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.
An electron and a positron moving at small speeds collide and annihilate each other. Find the energy of the resulting gamma photon.
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?
What is the kinetic energy of an electron in electron volts with mass equal to double its rest mass?
Find the speed at which the kinetic energy of a particle will differ by 1% from its nonrelativistic value \[\frac{1}{2} m_o v^2 .\]
