Question

When a planet moves in a circular orbit about the sun, the radius of its path is given by
3
√
T
2
K
, where T is the time period of the orbit and K is a constant equal to
2.97
×
10
−
19
. If the time period is multiplied by a factor of 8, which statement is true?


The radius is multiplied by a factor of 4.


The radius is multiplied by a factor of 8.


The radius is multiplied by a factor of 16.


The radius is multiplied by a factor of 64.

Answer 1

r = (T^2 / K)^{1/3} ∝ T^{2/3}. If T → 8T, the factor is 8^{2/3} = (2^3)^{2/3} = 2^2 = 4.

So the radius is multiplied by 4.