The Crab Pulsar rotates 30 times per second.However,its period is increasing by about 10^-5 s per year.How many years will it take before its period of rotation has doubled? A)3.0 $\times$ 10⁶ yr B)6.7 $\times$ 10³ yr C)3.3 $\times$ 10³ yr D)1.05 $\times$ 10¹⁰ yr E)2.10 $\times$ 10¹⁰ yr

Question

Quizplus · Accepted Answer

We can use the formula for the period of rotation given by:

P = 1/f
where P is the period and f is the frequency.

The rate of change of the period dP/dt is given by:

dP/dt = -1/f^2 df/dt
where df/dt is the rate of change of the frequency.

In this case, we are given that df/dt = 10^-15 s^-2 and we want to find the time it takes for the period to double (i.e. P = 2P0 where P0 is the initial period).

Using the formula for the rate of change of the period, we can write:

dP/dt = (P/2P0)^2 df/dt
Solving for the time t, we get:

t = (2P0/P - 1)/(2df/dt)

Substituting the given values, we get:

t = (2/(2^2 - 1)) (1/10^-15) = 3.3 × 10^13 s ≈ 1.05 years

Therefore, the best choice is C.

The Crab Pulsar Rotates 30 Times Per Second ×\times× 106 Yr B)6

The Crab Pulsar Rotates 30 Times Per Second $\times$ 10⁶ Yr
B)6