Gravitation

Question : 23

Total: 25

A star 2.5 times the mass of the sun and collapsed to a size of 12 km rotates with a speed of 1.2 rev. per second. (Extremely compact stars of this kind are known as neutron stars. Certain stellar objects called pulsars belong to this category). Will an object placed on its equator remain stuck to its surface due to gravity?
(mass of the sun =2×1030 kg).

Solution:

The object will remain stuck to the surface of star due to gravity, if the acceleration due to gravity is more than the centrifugal acceleration due to its rotation.
Acceleration due to gravity,
g=

6.67×10−11×2.5×2×1030

(12000)2

=2.3×1012ms−2
Centrifugal acceleration =rω2=r(2πv)2 =12000(2π×1.5)2 =1.1×106ms−2
Since g>rω2, therefore the body will remain stuck with the surface of star.

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