AP EAMCET · PHYSICS · Gravitation
A uniform solid sphere of mass \(M\) and radius ' \(a\) ' is surrounded by a concentric uniform thin spherical shell of mass \(0.5 \mathrm{M}\) and radius \(1.5 \mathrm{a}\). The gravitational potential energy of a unit mass kept at a distance of \(2.5 \mathrm{a}\) from the center is
- A \(\frac{-3 \mathrm{GM}}{5 \mathrm{a}}\)
- B \(\frac{3 \mathrm{GM}}{5 \mathrm{a}}\)
- C \(\frac{2 \mathrm{GM}}{5 \mathrm{a}}\)
- D \(\frac{-2 \mathrm{GM}}{5 \mathrm{a}}\)
Answer & Solution
Correct Answer
(A) \(\frac{-3 \mathrm{GM}}{5 \mathrm{a}}\)
Step-by-step Solution
Detailed explanation
The gravitational potential energy at a distance of \(2.5 \mathrm{a}\) is \(\mathrm{U}=-\frac{\mathrm{G}(\mathrm{M}+0.5 \mathrm{~m})}{2.5 \mathrm{a}}=-\frac{1.5 \mathrm{GM}}{2.5 \mathrm{a}}=-\frac{3 \mathrm{GM}}{5 \mathrm{a}}\)
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