Chapter 13: Q21P (page 380)

Certain neutron stars (extremely dense stars) are believed to be rotating at about $1 rev / s$ . If such a star has a radius of $20 km$ , what must be its minimum mass so that material on its surface remains in place during the rapid rotation?

Short Answer

Expert verified

Mass of the material on the surface of the neutron star is $5 \times 10^{24} kg$

Step by step solution

The given data

1) Frequency of rotation of neutron star is

$f = 1 \frac{r e v}{s}$

2)Radius of neutron star is $R = 20000 m$

Understanding the concept of Differential acceleration equation

We use the acceleration difference equation to find the mass of the material on the surface of the neutron star.

Formula:

Acceleration difference equation due to revolution, $g = a_{g} - ω^{2} R$ ... (i)

Calculation of the mass of the material

From equation (i), we can get

$a_{g} = \frac{G M}{R^{2}}$

To stay stationary on the surface of the neutron star, forces should be balanced so that, g= 0.

Hence substituting g=0 in equation (i), we get

$\begin{matrix} 0 = \frac{G M}{R^{2}} - ω^{2} R \\ \frac{G M}{R^{2}} = ω^{2} R \\ M = \frac{ω^{2} R^{3}}{G} \end{matrix}$

Substituting the values of $ω = 2 π f and R = 20000 m$ we get,

$\begin{matrix} M = \frac{{(2 π \times 1 \frac{rev}{s})}^{2} {(20000 m)}^{3}}{6.67 \times 10^{- 11} {Nm}^{2} {/kg}^{2}} \\ = 4.7 \times 10^{24} \\ \approx 5 \times 10^{24} kg \end{matrix}$

The mass of the material on the neutron star should be $5 \times 10^{24} kg$ .

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Certain neutron stars (extremely dense stars) are believed to be rotating at about $1 rev / s$ . If such a star has a radius of $20 km$ , what must be its minimum mass so that material on its surface remains in place during the rapid rotation?

Short Answer

Step by step solution

The given data

Understanding the concept of Differential acceleration equation

Calculation of the mass of the material

One App. One Place for Learning.

Most popular questions from this chapter

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Study anywhere. Anytime. Across all devices.

Certain neutron stars (extremely dense stars) are believed to be rotating at about1rev/s. If such a star has a radius of20 km, what must be its minimum mass so that material on its surface remains in place during the rapid rotation?

Short Answer

Step by step solution

The given data

Understanding the concept of Differential acceleration equation

Calculation of the mass of the material

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Solid State Physics

Force

Torque and Rotational Motion

Measurements

Fundamentals of Physics

Energy Physics

Study anywhere. Anytime. Across all devices.

Certain neutron stars (extremely dense stars) are believed to be rotating at about $1 rev / s$ . If such a star has a radius of $20 km$ , what must be its minimum mass so that material on its surface remains in place during the rapid rotation?