The gravitational potential strictly at the center of a solid, uniform Earth of mass M and radius R is:
A. Zero
B. -3GM / 2R
C. -GM / 2R
D. -GM / R
Answer: Option B
Solution (By JKSSB Mock Tests)
The gravitational potential V inside a uniform solid sphere at a distance r from the center is V = -GM * (3R^2 - r^2) / (2R^3). At the exact center of the Earth, r = 0. Substituting r = 0 gives V = -GM(3R^2) / 2R^3 = -3GM / 2R. The potential is strictly non-zero and highly negative.
Explanation:
A rocket works on the principle of conservation of linear momentum. As the exhaust gases are expelled downward at high velocity, they carry downward momentum. To conserve the total momentum of the system (which is initially zero), the rocket must acquire an equal and opposite (upward) momentum, propelling it forward.
Explanation:
Superconductivity occurs in certain materials below a critical temperature T_c, where electrical resistance drops abruptly to zero, and magnetic fields are expelled (Meissner effect). Option B describes insulators; C and D are unrelated. Memory aid: 'Superconductor: R=0 below T_c; perfect diamagnetism'. This modern physics concept is frequently tested in competitive exams. Always distinguish superconductivity (zero resistance) from perfect conductivity (theoretical limit); real superconductors exhibit Meissner effect, a defining property.
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