The Total solution for NCERT class 6-12
A star 2.5 times the mass of the sun andcollapsed to a size of 12 km rotates with a speed of 1.2 rev. per second. (Extremelycompact stars of this kind are known as neutron stars. Certain stellar objectscalled pulsars belong to this category). Will an object placed on its equatorremain stuck to its surface due to gravity? (Mass of the sun = 2 ├Ч 1030┬аkg).
Answer:┬аYes
A body gets stuck to thesurface of a star if the inward gravitational force is greater than the outwardcentrifugal force caused by the rotation of the star.
Gravitational force,┬аfg
Where,
M┬а= Mass of the star = 2.5 ├Ч 2 ├Ч 1030┬а= 5 ├Ч 1030┬аkg
m┬а= Mass of the body
R =┬аRadius of the star = 12 km = 1.2 ├Ч104┬аm
Centrifugal force,┬аfc┬а=┬аmr╧Й2┬а╧Й┬а=Angular speed = 2╧А╬╜
╬╜ = Angular frequency = 1.2 rev sтАУ1
fc┬а=┬аmR┬а(2╧А╬╜)2
=┬аm┬а├Ч (1.2 ├Ч104) ├Ч 4 ├Ч (3.14)2┬а├Ч (1.2)2┬а= 1.7 ├Ч105m┬аN
Since┬аfg┬а>┬аfc, the body will remainstuck to the surface of the star.