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Answer 1

Question

The distance between two planets (Neptune & Saturn) from Sun are 10^13 and 10^12 respectively. The ratio of time period of revolution around sun from the planet is

a) 100

b) 1/√10

c) √10

d) 10√10

Solution

According to Kepler's Third law:

T² ∝ R³

For Neptune: R is 10^13

(T1)² ∝ (10^13)³

T1 ∝ (10^13)³/² ...........(1st equation)

For Saturn: R is 10^12

(T2)² ∝ (10^12)³

T2 ∝ (10^12)³/² ...........(2nd equation)

We have to find their ratio. So, divide (1st equation) and (2nd equation)

T1/T2 = [(10^13)³/²]/[(10^12)³/²]

T1/T2 = [(10^13)/(10^12)]³/²

T1/T2 = (10)³/²

T1/T2 = 10√10

Therefore, The ratio of time period of revolution around sun from the planet is 10√10.

Option d) 10√10

Kepler's Third Law:

The square of time period of revolution of planet around sun is directly proportional to square of cube of length of semi-major axis. i.e. T² ∝ R³

For two planets, we can write it like, (T1)² ∝ (R1)³ and (T2)² ∝ (R2)³