A spacecraft travels past Earth and Mars in a straight line at a speed v = 0.8c at an instant when Earth and Mars are 2.4 × 1011 m apart; the distance being measured in the fixed frame of reference in which Earth and Mars are at rest. How far apart are Earth and Mars in the frame of the spacecraft? In the frame of the spacecraft, how much time elapses between the spacecraft crossing Earth and the spacecraft reaching Mars?
This problem involves length contraction and time dilation in special relativity. ### Given: - Speed of the spacecraft: \( v = 0.8c \) - Proper distance between Earth and Mars (rest frame): \( L_0 = 2.4 \times 10^{11} \) m - Speed of light: \( c \) ### Step __________ ____ _______ ____ _____ ___ _________.
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एक क्वांटम यांत्रिकीय संकारक A के आइगेन मान और आइगेन फलन क्रमशः anऔर Ψn है। यदि f(x) एक ऐसा फलन है जिसका प्रसार x की घात के पदों में हो सकता है तो सिद्ध करें कि :
Two spacecrafts A and B moving in opposite directions are each approaching the moon with speeds of 2.2 × 108 ms-1 and 2.5 × 108 ms-1 , respectively, as observed by an observer on the moon. Calculate the speed of A with which it is
(i) approaching the moon, and
(ii) approaching B, as observed by an observer in A.
Using Heisenberg’s Uncertainty Principle explain whether a particle trapped inside a one dimensional box of finite length can be at rest.
लिथियम नाभिक (L₁) के लिए द्रव्यमान क्षति और प्रति न्यूक्लिऑन बंधन ऊर्जा की गणना करें। दिया है:
लिथियम नाभिक का द्रव्यमान (M) 7.000000 u
प्रोटॉन का द्रव्यमान (mp) = 1.008665 u
न्यूटॉन का द्रव्यमान (m) = 1.007825 u
1 u = 931 मेव
Draw a curve of binding energy per nucleon as a function of mass number. With the help of this curve, explain the process of fission and fusion.
Calculate the expectation value of the kinetic energy of a simple harmonic oscillator in its ground state.
A spacecraft travels past Earth and Mars in a straight line at a speed v = 0.8c at an instant when Earth and Mars are 2.4 × 1011 m apart; the distance being measured in the fixed frame of reference in which Earth and Mars are at rest. How far apart are Earth and Mars in the frame of the spacecraft? In the frame of the spacecraft, how much time elapses between the spacecraft crossing Earth and the spacecraft reaching Mars?