A star 2.5 times the mass of the sun and coll | vedclass

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Question

(A) body remains stuck to the surface of a star if the inward gravitational force is greater than the outward centrifugal force caused by the rotation

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Yes

Vedclass · Answer

(A) body remains stuck to the surface of a star if the inward gravitational force is greater than the outward centrifugal force caused by the rotation of the star.Gravitational force,$f_g = \frac{GMm}{R^2}$Where,$M = 	ext{Mass of the star} = 2.5 	imes 2 	imes 10^{30} = 5 	imes 10^{30} \;kg$$m = 	ext{Mass of the body}$$R = 	ext{Radius of the star} = 12 \;km = 1.2 	imes 10^4 \;m$$G = 6.67 	imes 10^{-11} \;N \cdot m^2/kg^2$$f_g = \frac{6.67 	imes 10^{-11} 	imes 5 	imes 10^{30} 	imes m}{(1.2 	imes 10^4)^2} \approx 2.31 	imes 10^{11} \;m \;N$Centrifugal force,$f_c = mR\omega^2$Where $\omega = 2\pi v$ and $v = 1.2 \;rev/s$$f_c = m 	imes (1.2 	imes 10^4) 	imes (2 	imes 3.14 	imes 1.2)^2$$f_c = m 	imes (1.2 	imes 10^4) 	imes (7.54)^2 \approx 6.82 	imes 10^5 \;m \;N$Since $f_g > f_c$,the gravitational force is much stronger than the centrifugal force. Therefore,the object will remain stuck to the surface of the star.

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