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 × 1030 kg).
Answer: Yes
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, fg
Where,
M = Mass of the star = 2.5 × 2 × 1030 = 5 × 1030 kg
m = Mass of the body
R = Radius of the star = 12 km = 1.2 ×104 m
Centrifugal force, fc = mrω2 ω =Angular speed = 2πν
ν = Angular frequency = 1.2 rev s–1
fc = mR (2πν)2
= m × (1.2 ×104) × 4 × (3.14)2 × (1.2)2 = 1.7 ×105m N
Since fg > fc, the body will remainstuck to the surface of the star.