The time taken for a radioactive sample to decay to 1/16th of its initial activity is:
A. 2 half-lives
B. 3 half-lives
C. 4 half-lives
D. 8 half-lives
Answer: Option C
Solution (By JKSSB Mock Tests)
After n half-lives, activity reduces to (1/2)ⁿ of initial. Set (1/2)ⁿ = 1/16 ⇒ (1/2)ⁿ = (1/2)⁴ ⇒ n = 4 half-lives. Thus time = 4 × half-life. Memory aid: '1/2ⁿ remaining after n half-lives; 1/16 = 1/2⁴ ⇒ 4 half-lives'. This radioactivity calculation is frequently tested in competitive exams. Always express fraction as power of 1/2 to find half-life count. This problem assesses understanding of exponential decay without heavy computation.
Explanation:
Power P = V²/R => R = V²/P = 200²/100 = 40000/100 = 400 Ω. Also current I = P/V = 0.5 A, R = V/I = 200/0.5 = 400 Ω. Use P = V²/R for direct calculation.
Explanation:
Light year: distance light travels in one year in vacuum ≈ 9.46×10¹⁵ m. Astronomical distance unit, not time. Memory aid: 'Light year = speed × time = distance'. Unit knowledge frequently tested in competitive exams to avoid common misconception about light year being time unit.
Explanation:
Area under v-t graph gives displacement (distance if velocity doesn't change sign). Slope of x-t gives velocity. Slope of v-t gives acceleration. Area a-t gives change in velocity.
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