Verified Solution • 2025–26 Session moderate

QJEEM18Ph14ab: JEE Main 2018 Physics - Class 11 JEEM18Ph14ab Solution: The relative uncertainly in the period of a satellite orbiting…

The relative uncertainly in the period of a satellite orbiting around the earth is 10-2. If the relative uncertainty in the radius of the orbit is negligible, the relative uncertainty in the mass of the earth is :

Multiple Choice Options

  • A 10 −- 2
  • B 2 ×\times 10 −- 2
  • C 3 ×\times 10 −- 2
  • D 6 ×\times 10 −- 2

Step-by-Step Verified Solution

From kepler's law,

T = 2 π\pi r3GM\sqrt {{{{r^3}} \over {GM}}}

⇒\Rightarrow    \,\,\, T2 = 4π2GMr3{{4{\pi ^2}} \over {GM}}{r^3}

⇒\Rightarrow    \,\,\, M = 4π2G×r3T2{{4{\pi ^2}} \over G} \times {{{r^3}} \over {{T^2}}}

∴   \therefore\,\,\, ΔMM{{\Delta M} \over M} = 2 ΔTT{{\Delta T} \over T} + 3 Δrr{{\Delta r} \over r}

as Δrr≃0{{\Delta r} \over r} \simeq 0

∴   \therefore\,\,\, ∣ΔMM∣\left| {{{\Delta M} \over M}} \right| = 2 ΔTT{{\Delta T} \over T} = 2 ×\times 10 −- 2

Related Learning Resources & Exam Preparation

JEE Main PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring