One day on a spacecraft corresponds to 2 days | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) According to the theory of special relativity, the time dilation formula is given by $T = \frac{T_0}{\sqrt{1 - \frac{v^2}{c^2}}}$, where $T$ is th

Vedclass · Accepted Answer

$2.6 	imes 10^8 \ m/s$

Vedclass · Answer

(C) According to the theory of special relativity, the time dilation formula is given by $T = \frac{T_0}{\sqrt{1 - \frac{v^2}{c^2}}}$, where $T$ is the time observed on Earth, $T_0$ is the proper time on the spacecraft, $v$ is the velocity of the spacecraft, and $c$ is the speed of light $(3 	imes 10^8 \ m/s)$.Given $T_0 = 1 \ day$ and $T = 2 \ days$, we have:$2 = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}$Squaring both sides: $4 = \frac{1}{1 - \frac{v^2}{c^2}}$$1 - \frac{v^2}{c^2} = \frac{1}{4} = 0.25$$\frac{v^2}{c^2} = 1 - 0.25 = 0.75$$v = c \sqrt{0.75} = 3 	imes 10^8 	imes 0.866 = 2.598 	imes 10^8 \ m/s \approx 2.6 	imes 10^8 \ m/s$.

One day on a spacecraft corresponds to $2$ days on the earth. The speed of the spacecraft relative to the earth is

Similar Questions

The anode voltage of a photocell is kept fixed. The wavelength $\lambda$ of the light falling on the cathode is gradually changed. The plate current $I$ of the photocell varies as follows:

The particle nature and wave nature of electromagnetic waves and electrons can be demonstrated by which of the following?

The anode voltage of a photocell is kept constant. The wavelength of the light incident on the cathode is changed gradually. Which of the following graphs represents the variation of the photoelectric current $(I)$ with the wavelength $(\lambda)$?

In a photoelectric experiment,light of wavelength $800 \ nm$ produces photoelectrons with the smallest de Broglie wavelength of $1 \ nm$. Then the work function of the metal used in the experiment is nearly (in $eV$)

Dual nature of light is exhibited by

Vedclass Test Series

Exam Paper Generator

Online Exam Module