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If the distance between the earth and the sun were half its present value, the number of days in a year would have been

(a) 64.5

(b) 129

(c) 182.5

(d) 730

in Physics
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## 1 Answer

+1 vote
Best answer

The correct answer is  129 days option b

Explaination :

BY keplers third law $$T^2 \propto R^3$$

$$\therefore { ({ T_2\over T_1})^2=({ R_2\over R_1})^3}$$

T= 365 days , R1 =R , R2 = R/2

$${ ({ T_2\over 365})^2=({{ R_2/2}\over R_1})^3}$$

$$T_2^2={(365)^2\over8}$$

$$T_2^2=16653$$   ----{note: $$129^2=16641$$ but 16653 is nearby 129 hence due to option answer is 129}

$$T_2=129 \space days$$

by Expert (10.9k points)