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The radius of our galaxy is about 3 xx 1...

The radius of our galaxy is about `3 xx 10 ^(20)m`.With what speed should a person travel so that he can reach from the centre of the galaxy to its edge in 20 years of his lifetime ?

Text Solution

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Let the speed of the person be v . As seen by the person, the edge of the galaxy is coming towards him at a speed v. In 20 years (as measured by the person ), the edge moves (20 y ) v and reaches the person. The radisu of the galaxy as measured by the person is , therefore , (20 y)v . The rest length of the radius of the galaxy is ` 3 xx 10^(20)m. ` Thus ,
` (20y )v = (3 xx 10^(20)m) (sqrt 1 - v ^(2)/ c^(2) `
or, (6 .312 xx 10 ^(8) s ) ^(2) v^(2) = (9 xx 10 ^(40) m ^(2)) (1- v^(2) / c^(2) )`.
Solving this,
v =0.9999996 c.
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