Q.

Keeping the mass of the earth as constant, if its radius is reduced to 1/4 th of its initial value, then the period of revolution of the earth about its own axis and passing through the centre (in hours) is (assume the earth to be a solid sphere and its initial period of rotation as 24 h) [EAMCET 2014]

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a

12

b

3

c

6

d

1.5

answer is A.

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Detailed Solution

As we know that,Time period of revolution of earth at initial condition,T=2πReg                         …(i)So, if radius is reduced,   R'=Re4Time period becomes   T'=2πRe4g                           …(ii)On dividing Eq. (i) by Eq. (ii), we getTT'=2πRe/g2πRe/4g=2⇒  T'=T2=242=12 h
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