Verified Solution • 2025–26 Session moderate

Q7.14: NCERT Physics - Part 1 GRAVITATION 7.14 Solution: A Saturn year is 29.5 times the earth year. How far is the…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students frequently invert the exponents in Kepler's third law, mistakenly calculating the distance ratio as $(29.5)^{2/3}$ instead of $(29.5)^{2/3}$ derived from $R^3 \propto T^2$. Ensure you isolate the radius by taking the cube root of the squared period ratio, not the square root of the cubed period ratio.

A Saturn year is 29.5 times the earth year. How far is the Saturn from the sun if the earth is 1.50×1081.50 \times 10^8 km away from the sun?

Step-by-Step Verified Solution

**Answer:** 1.43×1091.43 \times 10^9 km **Step-by-Step Explanation:** Using Kepler's third law:
(RSRE)3=(TSTE)2=(29.5)2=870.25\left(\frac{R_S}{R_E}\right)^3 = \left(\frac{T_S}{T_E}\right)^2 = (29.5)^2 = 870.25
RSRE=(870.25)1/3=9.55\frac{R_S}{R_E} = (870.25)^{1/3} = 9.55
RS=9.55×1.5×108=1.43×109 kmR_S = 9.55 \times 1.5 \times 10^8 = 1.43 \times 10^9 \text{ km}
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All Questions in this Chapter

Q7.1 Q7.2 Q7.3 Q7.4 Q7.5 Q7.6 Q7.7 Q7.8 Q7.9 Q7.10 Q7.11 Q7.12 Q7.13 Q7.14 Q7.15 Q7.16 Q7.17 Q7.18 Q7.19 Q7.20 Q7.21

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