Question

if the mass of the earth is doubled and the distance of the moon revolving around the earth is also doubled ,then find the new time period of revolution of moon .(take the present time of revolution as 28 days).

Answer 1

new time period of revolution of the moon is 56 days.

we know, time period is given as , T = 2π√{r³/GM}

for time period of moon revolving around the earth,

r is the distance of moon revolving around the earth , M is mass of the earth, G is gravitational constant.

so, T ∝ √(r³/M)

⇒T1/T2 = √(r1/r2)³ × √(M2/M1)

given, T1 = 28 days, M2 = 2M1 , r2 = 2r1

then, 28 days/T2 = √(1/2)³ × √(2)

⇒28/T2 = √{1/8 × 2} = 1/2

⇒T2 = 56 days

hence, new time period of revolution of the moon is 56 days

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Answer 2

$\huge\bold\purple{Answer:-}$

we know, time period is given as , T = 2π√{r³/GM}

for time period of moon revolving around the earth,

r is the distance of moon revolving around the earth , M is mass of the earth, G is gravitational constant.

so, T ∝ √(r³/M)

⇒T1/T2 = √(r1/r2)³ × √(M2/M1)

given, T1 = 28 days, M2 = 2M1 , r2 = 2r1

then, 28 days/T2 = √(1/2)³ × √(2)

⇒28/T2 = √{1/8 × 2} = 1/2

⇒T2 = 56 days

hence, new time period of revolution of the moon is 56 days