Ncert Exercises & Solutions

8.23 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).

An object will get stuck at the star's surface if the centrifugal force of the star is less than the gravitational force.

An object placed on the equator will remain stuck to its surface if t

G i v e n,

M = 2.5 \times 2 \times 10^{30} = 5 \times 10^{30} k g .

R = 12 k m = 12000 m

ω = 1.5 r p s = 3 π r a d / s

N o w,

F_{G} = \frac{G M m}{R^{2}} = \frac{6.67 \times 10^{- 11} \times 5 \times 10^{30} \times m}{{(12 \times 10^{3})}^{2}}

= (2.3 \times 10^{12} m) N .

F_{C} = m r ω^{2} = m \times 12 \times 10^{3} \times {(3 π)}^{2}

= 1.06 \times 10^{6} m N .

A s F_{G} > F_{C} T h e r e f o r e t h e o b j e c t w i l l r e m a i n s t u c k .

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