A person travelling by a car moving at `100 km h^(-1)` finds that his wristwatch agress with the clock in a tower A. By what amount will his wristwatch lag or lead the clock on another tower B, 1000km (in the earth's frame ) from the tower A when the car reaches there?

Explanation

Here ` v = 100 km / h` ,
`Delta t = proper time interval `
` = 0.6 s^(-1) `
` Delta t' = Delat t / (sqrt 1 - V^(2)/ c^(2)) `
` = (sqrt (10 xx 3600 ) / 1 - (1000 / 36 xx 3xx10^(8)^(2)))`
` Delta t ' = 10 xx 3600 [ 1 - (1000 / 36 xx 3 xx 10^(8) )^(2) ]^(-1/2) Delta t `
by solving We get,
` Delta t - Deltat ' = 0.154 ns `
`:.` Time will lag by 0.154 ns ` .