Verified Solution • 2025–26 Session moderate

QJEEM24Ph107e: JEE Main 2024 Physics - Class 11 JEEM24Ph107e Solution: A planet takes 200 days to complete one revolution around the…

A planet takes 200 days to complete one revolution around the Sun. If the distance of the planet from Sun is reduced to one fourth of the original distance, how many days will it take to complete one revolution :

Multiple Choice Options

  • A 20
  • B 50
  • C 100
  • D 25

Step-by-Step Verified Solution

amp;T2∝r3amp;T12r13=T22r23amp;(200)2r3=T22(r4)3amp;200×2004×4×4=T22amp; T2=2004×2amp; T2=25 days \begin{aligned}& \mathrm{T}^2 \propto \mathrm{r}^3 \\& \frac{\mathrm{T}_1^2}{\mathrm{r}_1^3}=\frac{\mathrm{T}_2^2}{\mathrm{r}_2^3} \\& \frac{(200)^2}{\mathrm{r}^3}=\frac{\mathrm{T}_2^2}{\left(\frac{\mathrm{r}}{4}\right)^3} \\& \frac{200 \times 200}{4 \times 4 \times 4}=\mathrm{T}_2^2 \\& \mathrm{~T}_2=\frac{200}{4 \times 2} \\& \mathrm{~T}_2=25 \text { days }\end{aligned}

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