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Q7.5: NCERT Physics - Part 1 GRAVITATION 7.5 Solution: Let us assume that our galaxy consists of stars each of one…

Let us assume that our galaxy consists of 2.5×10112.5 \times 10^{11} stars each of one solar mass. How long will a star at a distance of 50,000 ly from the galactic centre take to complete one revolution? Take the diameter of the Milky Way to be 10510^5 ly.

Step-by-Step Verified Solution

**Answer:** The star takes about 3.55×1083.55 \times 10^8 years to complete one revolution. **Step-by-Step Explanation:** Mass of galaxy M=2.5×1011×2×1030=5×1041M = 2.5 \times 10^{11} \times 2 \times 10^{30} = 5 \times 10^{41} kg. Radius of orbit r=50000r = 50000 ly =50000×9.46×1015=4.73×1020= 50000 \times 9.46 \times 10^{15} = 4.73 \times 10^{20} m. Using T2=4π2r3GMT^2 = \frac{4\pi^2 r^3}{GM}:
T=4π2(4.73×1020)36.67×10−11×5×1041≈1.12×1016 sT = \sqrt{\frac{4\pi^2 (4.73 \times 10^{20})^3}{6.67 \times 10^{-11} \times 5 \times 10^{41}}} \approx 1.12 \times 10^{16} \text{ s}
Converting to years:
T=1.12×1016365.25×24×3600≈3.55×108 yearsT = \frac{1.12 \times 10^{16}}{365.25 \times 24 \times 3600} \approx 3.55 \times 10^8 \text{ years}
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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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