The acceleration due to gravity on Earth's surface is g. At a height equal to Earth's radius above the surface, g' will be: MCQ with Answer and Explanation
The acceleration due to gravity on Earth's surface is g. At a height equal to Earth's radius above the surface, g' will be:
A. g/2
B. 2g
C. g/4
D. g/9
Answer: Option C
Solution (By JKSSB Mock Tests)
Acceleration due to gravity at height h: g' = gR²/(R+h)², where R is Earth's radius. Given h = R, so g' = gR²/(2R)² = gR²/4R² = g/4. This inverse square law dependence arises from Newton's law of gravitation. At depth, variation differs, but for height, this formula applies. Memory aid: Double the distance from center ⇒ gravity becomes one-fourth. This standard result is frequently tested in gravitation sections of competitive exams. Always verify whether height or depth is specified, as formulas differ significantly.
Explanation:
Fuse melts and breaks circuit when current exceeds rating. MCB (Miniature Circuit Breaker) does same but resettable. Switch only turns on/off. Resistor limits current but doesn't break.
Assertion (A): When ice floats in water, its approximately 1/10th volume remains outside the water. Reason (R): The density of ice is approximately 10% less than the density of water.
A.A is true but R is false.
B.A is false but R is true.
C.Both A and R are true and R is the correct explanation of A.
D.Both A and R are true but R is NOT the correct explanation of A.
Explanation:
The density of ice is about 900 kg/m³ (0.9 g/cm³), while pure water is 1000 kg/m³ (1.0 g/cm³). According to the principle of floatation, the fraction of volume submerged is the ratio of densities: ρ_ice / ρ_water = 0.9. This means 90% is submerged, leaving exactly 10% (1/10th) exposed above the surface. Reason R explains Assertion A.
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