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JIPMER 2006
Exam
JIPMER
Year
2006
Subject
Physics
Chapter
Gravitation

JIPMER 2006 · Physics · Gravitation

Earth is revolving around the sun. If the distance of the earth...

Earth is revolving around the sun. If the distance of the earth from the sun is reduced to 1/41 / 4 th of the present distance then the length of present day will be reduced by :

Options

  1. A14\frac{1}{4}
  2. B12\frac{1}{2}
  3. C18\frac{1}{8}
  4. D16\frac{1}{6}

Correct answer

C. 18\frac{1}{8}

Step-by-step solution

From Kepler's law T2∝R3∴(T1T2)2=(R1R2)3T1T2=(R1R2)3/2=(RR/4)3/2=(4)3/2=(2)3=8∴T2=T18\begin{aligned} & T^2 \propto R^3 \\ & \therefore \quad\left(\frac{T_1}{T_2}\right)^2=\left(\frac{R_1}{R_2}\right)^3 \\ & \frac{T_1}{T_2}=\left(\frac{R_1}{R_2}\right)^{3 / 2}=\left(\frac{R}{R / 4}\right)^{3 / 2} \\ & =(4)^{3 / 2}=(2)^3=8 \\ & \therefore \quad T_2=\frac{T_1}{8} \\ & \end{aligned} Hence, the length of the day is reduced by 18\frac{1}{8}.
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