Question

A clock keeps correct time, at what speed should it move relative to observer so that it looses 1 minute in 24 hours

a) 1.1m/sec
b) 2.3m/sec
c) 2.3 m/sec
d) 0.1m/sec

URGENT​

Answer 1

Answer:

answer is given in above pic

Answer 2

Answer:

None of the given option is correct.

Correct answer is $1.1178\times 10^7\ m/s.$

Explanation:

Time dilation is a phenomenon in which a moving clock runs slow.

The time interval $t$ of an event in a rest frame and the time interval of the same event in the frame of clock $t_o$ are related as

$t_o = \gamma t$.

where,

• $\gamma = \dfrac{1}{\sqrt{1-\dfrac {v^2 }{c^2}}}$.

• $v$ = speed of the clock.

• $c$ = speed of light in vacuum = $3\times 10^8\ \rm m/s$.

Now it is given that the clock looses 1 minute in 24 hours, therefore,

$\rm t= 24\ hours = 24\times 3600\ seconds = 86400\ seconds.\\t_o = 24\ hours - 1 minute = 86400-60=86340\ seconds.$

Using the equation of time dilation,$86400=\dfrac{1}{\sqrt{1-\dfrac{v^2}{c^2}}} 86340\\\sqrt{1-\dfrac{v^2}{c^2}}=\dfrac{86340}{86400}=0.999305556\\1-\dfrac{v^2}{c^2}=(0.999305556)^2=0.99861\\\dfrac{v^2}{c^2} = 1-0.99861=1.3884\times 10^{-3}\\\dfrac vc = \sqrt{1.3884\times 10^{-3}}=3.726\times 10^{-2}\\v=3.726\times 10^{-2}\times c = 3.726\times 10^{-2}\times 3\times 10^8 = 1.1178\times 10^7\ m/s.$

Thus, no option is correct.