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What is the minimum energy needed to launch a satellite of mass $m$ from the surface of a planet of mass $M$ and radius $R$ into a circular orbit at altitude $2R$?
The orbit radius is $r = R + 2R = 3R$.
Orbital KE: $KE = \frac{GmM}{2r} = \frac{GmM}{6R}$
Total mechanical energy in orbit: $E_{orbit} = -\frac{GmM}{2r} = -\frac{GmM}{6R}$
Energy on surface: $E_{surface} = -\frac{GmM}{R}$
Minimum energy required:
$\Delta E = E_{orbit} - E_{surface} = -\frac{GmM}{6R} + \frac{GmM}{R} = \frac{GmM}{R}\left(1 - \frac{1}{6}\right) = \frac{5GmM}{6R}$
\(\Delta v = \dfrac{1 \times 10^{-18}}{9 \times 10^{-28}} = \dfrac{1}{9} \times 10^{10} \approx 1 \times 10^9\) cm s\(^{-1}\)
This enormously large uncertainty in velocity illustrates why classical mechanics fails for electrons β they cannot have precisely defined trajectories.
CTG classification is based on NICE (2022) / FIGO guidelines. Assess 4 features:
| Feature | Reassuring | Non-reassuring | Abnormal | This Strip |
|---|---|---|---|---|
| Baseline FHR | 110β160 bpm | 100β109 or 161β180 | <100 or >180 | 155 bpm β Reassuring |
| Variability | 5β25 bpm | 3β4 bpm (>30 min) or >25 bpm | <3 bpm (>60 min) or sinusoidal | 2 bpm = Abnormal |
| Decelerations | None or early | Variable (typical) | Late decelerations | Late = Abnormal |
| Accelerations | Present | Absent | β | Not mentioned |
Classification (NICE):
- Normal: All 4 features reassuring
- Suspicious: 1 non-reassuring feature
- Pathological: β₯2 non-reassuring OR β₯1 abnormal feature
This CTG has: variability 2 bpm (abnormal) + late decelerations (abnormal) = PATHOLOGICAL
Action: Inform senior doctor immediately, consider fetal blood sampling (FBS), prepare for expedited delivery. Offer resuscitative measures: maternal lateral position, IV fluids, stop oxytocin.
IIMA, Ahmedabad:
- Architect: Louis I. Kahn (American architect), with later campus additions by Balkrishna Doshi.
- Period: 1962β1974
- Material: Exposed red brick β creating a warm, monumental campus.
- Features circular stairways framed by bold brick arches, dramatic light play.
- Kahn also designed the National Assembly of Bangladesh (Dhaka) using a similar vocabulary.
This is a masterpiece of modern institutional architecture in India.
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