Question

13. A satellite moving in a circular path of radius
'r around earth has a time period T. If its
radius slightly increases by 4%, then
percentage change in its time period is
1) 1% 2)6% 3) 3% 4) 9%​

Answer 1

answer : option (2) 6%

time period of satellite moving around earth is given as , T = 2π√{r³/GM}

means, Time period is directly proportional to r^(3/2) .

i.e., T ∝ r^(3/2)

so, To find error in time period

using formula,

∆T/T = (3/2) × ∆r/r

or, % error in T = (3/2) × % error in r

given, % change in r = % error in r = 4%

so, % error in T = (3/2) × 4 = 6%

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Answer 2

$\bf\large\underline\green{Answer:-}$

2)6