Question

The distance of two planets from the sun are 10¹³ m and 10¹² m respectively. The ratio of time periods of the planets is

(a) √10

(b) 10√10

(c) 10 

(d) 1/√ 10

Answer 1

Correct option (b) 10√10

Explanation:

Distance of two planets from sun, r₁ = 10¹³m and r₂ = 10¹²m.

Relation between time period (T) and distance of the planet from the sun is

T² ∝ r³  or T ∝ r^3/2.

Therefore T₁/T₂ = (r₁/r₂)^3/2 = (10^13_/10¹²)^3/2 = 10^3/2

= 10√10.