Gravitational Acceleration Differences in a Pulsar: Calculation and Comparison

[wcase]

Here is the question:

Consider a pulsar, a collapsed star of extremely high density, with a mass M equal to that of the Sun (1.98 × 1030 kg), a radius R of only 12.7 km, and a rotational period T of 0.0545 s. By what percentage does the free-fall acceleration g differ from the gravitational acceleration a_g at the equator of this spherical star?

Just to make sure I am doing it right, I have the equations
a_g=GM/R^2
g=a_g-w²R

and when I plug in the values I get a_g=8.1881*10¹⁷
g=8.18642*10¹¹

From what I gather from my textbook, a_g is the gravitational acceleration and g is the free-fall.

Now my predicament is that this is homework submitted online, I have a certain amount of submissions, and I only have one remaining.

So when I compare the percentages, should I do a_g/g*100=1.0002*10⁸%
or g/a_g*100=.0001%

Thanks

 

[jedishrfu]

your problem mentions differ so I think you need to calculate a difference ( (g - ag) / g) *100 but that's just my guess.

 

[wcase]

that makes sense, but now I have to choose from ((g-ag)/g)*100=-1.0002e8 and
((ag-g)/ag)*100=99.9999

but I guess since subtraction isn't reversible, it is most likely ((g-ag)/g)

 

[malemdk]

In the above problem accelaration increases so (ag-g)/g*100 is the correct answer

 

[wcase]

"(ag-g)/g*100 is the correct answer"

Indeed, thanks.