Binding energy per nucleon peaks at: MCQ with Answer and Explanation
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Question #1
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The half-life of a radioactive substance is 10 days. After 30 days, the fraction remaining undecayed is:
Correct Answer: Option C
Explanation:
Number of half-lives n = total time / half-life = 30 days / 10 days = 3. Fraction remaining = (1/2)ⁿ = (1/2)³ = 1/8. This exponential decay law is fundamental in radioactivity. Memory tip: 'After n half-lives, fraction = 1/2ⁿ'. Competitive exams frequently test such calculations with varying time intervals. Always compute number of half-lives first. Note: Activity (decays per second) also reduces by same fraction. This problem assesses understanding of half-life concept beyond rote memorization.
Number of half-lives n = total time / half-life = 30 days / 10 days = 3. Fraction remaining = (1/2)ⁿ = (1/2)³ = 1/8. This exponential decay law is fundamental in radioactivity. Memory tip: 'After n half-lives, fraction = 1/2ⁿ'. Competitive exams frequently test such calculations with varying time intervals. Always compute number of half-lives first. Note: Activity (decays per second) also reduces by same fraction. This problem assesses understanding of half-life concept beyond rote memorization.
Question #2
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A car's speedometer measures:
Correct Answer: Option A
Explanation:
A speedometer shows the speed of a vehicle at a particular instant in time. Speed is a scalar quantity (magnitude only, no direction). Therefore, it measures instantaneous speed. If it were measuring velocity, it would also need to display the car's current compass direction of travel at every moment.
A speedometer shows the speed of a vehicle at a particular instant in time. Speed is a scalar quantity (magnitude only, no direction). Therefore, it measures instantaneous speed. If it were measuring velocity, it would also need to display the car's current compass direction of travel at every moment.
Question #3
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The focal length of a spherical mirror is related to its radius of curvature R by:
Correct Answer: Option A
Explanation:
For spherical mirrors (concave or convex), focal length f = R/2, where R is radius of curvature. This holds under paraxial approximation (small angles). Derivation uses geometry of reflection and small-angle approximations. Memory tip: 'Mirror: f = R/2; Lens: 1/f = (n-1)(1/R₁ - 1/R₂)'. This fundamental relation is frequently tested in optics sections of competitive exams. Always note sign conventions: f negative for convex mirrors, positive for concave; R follows same sign as f.
For spherical mirrors (concave or convex), focal length f = R/2, where R is radius of curvature. This holds under paraxial approximation (small angles). Derivation uses geometry of reflection and small-angle approximations. Memory tip: 'Mirror: f = R/2; Lens: 1/f = (n-1)(1/R₁ - 1/R₂)'. This fundamental relation is frequently tested in optics sections of competitive exams. Always note sign conventions: f negative for convex mirrors, positive for concave; R follows same sign as f.
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