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Suppose the sun shrank from its present ...

Suppose the sun shrank from its present size so that its radius is halved. Whaat would energy? (Given that mass of Sun=`1.989xx10^(30)`kg and the radius of the Sun =`6.95xx10^(8)`m)

A

`4.321xx10^(50) J`

B

`2.275xx10^(41) J`

C

`1.102xx10^(30) J`

D

`8.123xx10^(10) J`

Text Solution

Verified by Experts

(b) Given,
`M=1.989xx30kg`
`R=6.95xx20^(8)m`
`G=6.66xx10^(-11)Nm^(2)kg^(2)`
Present gravitational energy of the Sun is given by
`V=(3)/(5)(GM^(2))/(R)`
In case Sun shrank from its present size till its radius is halved `((R)/(2))`,then
`V'=(3)/(5)(GM^(2))/(R//2)=(6)/(5)(GM^(2))/(R^(2))`
`therefore` Change in gravitational potential energy of the Sun
`V-V'=-(3)/(5)cdot(GM^(2))/(R)-(-(6)/(5)cdot(GM^(2))/(R))`
`V-V'=-(3)/(5)cdot(GM^(2))/(R)=(3)/(5)xx(6.66xx10^(-11)xx(1.989xx10^(30))^(2))/(6.95xx10^(8))`
`=2.275xx10^(41)`J
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