Question

During most of its lifetime, a star maintains anequilibriumsize in which the inward force of gravity on each atomis balancedby an outward pressure force due to the heat of thenuclearreactions in the core. But after all the hydrogen "fuel"isconsumed by nuclear fusion, the pressure force drops and thestarundergoes a gravitational collapse until it becomesaneutron star. In a neutron star, the electrons andprotonsof the atoms are squeezed together by gravity until theyfuse intoneutrons. Neutron stars spin very rapidly and emit intensepulsesof radio and light waves, one pulse per rotation. These"pulsingstars" were discovered in the 1960s and arecalledpulsars.

1.A star with the mass (M= 2.0 x 10^30) and size (R= 3.5x10^8) of our sun rotates once every 35.0 days. Afterundergoinggravitational collapse, the star forms a pulsar that isobserved byastronomers to emit radio pulses every 0.200s. Bytreating theneutron star as a solid sphere, deduce itsradius.

2.What is the speed of a point on the equator of theneutronstar? Your answer will be somewhat too large because a starcannotbe accurately modeled as a solid sphere.