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Q.

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

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a

\large 1.5 \times {10^8}m{s^{ - 1}}

b

\large 2.1 \times {10^8}m{s^{ - 1}}

c

\large 2.6 \times {10^8}m{s^{ - 1}}

d

\large 5.2 \times {10^8}m{s^{ - 1}}

answer is C.

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Detailed Solution

\large T = \frac{{{T_0}}}{{{{[1 - ({v^2}/{c^2})]}^{1/2}}}}
 By substituting  T0 = 1 day and T = 2 days we get
\large v = 2.6 \times {10^8}\,m{s^{ - 1}}

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