If the error in measurement of radius of a sphere is 2%, the percentage error in the calculated volume of the sphere will be: MCQ with Answer and Explanation
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Question #1
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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:
Correct Answer: Option A
Explanation:
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.
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.
Question #2
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The slope of a displacement-time graph for uniform motion is
Correct Answer: Option C
Explanation:
Displacement-time graph slope = Δx/Δt = average velocity. For uniform motion, velocity constant, graph is a straight line, slope equals velocity. Acceleration would be slope of velocity-time graph. Thus, slope represents velocity. Exam trick: slope of x-t graph gives instantaneous velocity.
Displacement-time graph slope = Δx/Δt = average velocity. For uniform motion, velocity constant, graph is a straight line, slope equals velocity. Acceleration would be slope of velocity-time graph. Thus, slope represents velocity. Exam trick: slope of x-t graph gives instantaneous velocity.
Question #3
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A 50 kg person climbs 30 steps each 15 cm high in 10 s. Power (g=10) is
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