Simple Pendulum

Answer: C. T = 2π√(L/g) does not contain mass. Doubling the bob mass has no effect on the period (NCERT Class 11 Physics, Chapter 13, page 271).

Why A is wrong: A is wrong because this implies the period halves with doubled mass — no mass term exists in the pendulum period formula.

Why B is wrong: B is wrong because this uses T' = T√2, as if T ∝ √m — mass does not appear in T = 2π√(L/g) (trap: assuming mass dependence).

Why D is wrong: D is wrong because this assumes T ∝ m (period doubles when mass doubles) — again, mass is absent from the formula (trap: assuming mass dependence).

Answer: C. T = 2π√(L/g) = 2π√(1.00/9.80) = 2π × 0.3194 = 2.007 s ≈ 2.01 s (NCERT Class 11 Physics, Chapter 13, page 271).

Why A is wrong: A is wrong because 1.00 s = π√(L/g) drops the factor of 2 from 2π (trap: dropping the 2π factor).

Why B is wrong: B is wrong because 0.32 s = √(L/g) omits the 2π factor entirely.

Why D is wrong: D is wrong because 6.28 s = 2π√L leaves g out of the square root; with L = 1.00 m, √L = 1 and the result is just 2π.

Answer: B. T = 2π√(L/g), so T ∝ √L. If L becomes 4L, T' = 2π√(4L/g) = 2 × 2π√(L/g) = 2T (NCERT Class 11 Physics, Chapter 13, page 271).

Why A is wrong: A is wrong because halving implies T ∝ 1/L, which is the inverse relationship — the actual dependence is T ∝ √L.

Why C is wrong: C is wrong because this would mean the period is independent of length, but T ∝ √L — length changes do affect the period (unlike mass changes).

Why D is wrong: D is wrong because this assumes T ∝ L (linear), but the square root gives T ∝ √L, so quadrupling L only doubles T (trap: using linear instead of square-root scaling).

Answer: B. A seconds pendulum has T = 2 s. From T = 2π√(L/g): L = gT²/(4π²) = 9.8 × 4 / (4 × 9.87) ≈ 0.993 m ≈ 1.00 m. This is a standard NCERT result (Chapter 14, page 268).

Why A is wrong: A is wrong because L = 0.25 m gives T = 2π√(0.25/9.8) ≈ 1.00 s — this is a half-seconds pendulum, not a seconds pendulum.

Why C is wrong: C is wrong because L = 2.00 m gives T = 2π√(2.00/9.8) ≈ 2.84 s, not 2.00 s — this confuses L with T numerically.

Why D is wrong: D is wrong because L = 4.00 m gives T = 2π√(4.00/9.8) ≈ 4.01 s — this uses T ∝ L instead of T ∝ √L (trap: linear scaling).

Answer: A. T ∝ 1/√g. Ratio g_Earth/g_Moon ≈ 9.8/1.63 ≈ 6.0. So T_Moon = T × √(g_Earth/g_Moon) = T√6 (NCERT Class 11 Physics, Chapter 13, page 271).

Why B is wrong: B is wrong because this assumes the period is independent of g, but g appears explicitly in T = 2π√(L/g) — reducing g increases T.

Why C is wrong: C is wrong because T/√6 implies T ∝ √g, which would mean the period decreases when g decreases — the opposite is true since T ∝ 1/√g.

Why D is wrong: D is wrong because 6T assumes T ∝ 1/g (linear inverse), but the square root gives T ∝ 1/√g, so the factor is √6, not 6 (trap: linear instead of square-root scaling).

Answer: B. T = 2π√(L/g) contains only the effective length and g. The mass cancels out of the equation of motion, so a heavy bob and a light bob on the same string keep the same period (NCERT Class 11 Physics, Chapter 13, page 271).

Why A is wrong: A is wrong because length does affect the period — T ∝ √L. Changing the string length changes the time period.

Why C is wrong: C is wrong because g directly affects the period — T ∝ 1/√g. Changing the location (and hence g) changes the time period.

Why D is wrong: D is wrong because that distance IS the effective length L — measured to the centre of the bob, not to its lower edge — so changing it changes T exactly as option A does (trap: not recognising the effective length when it is spelled out in words).

Answer: D. T ∝ √L, so T'/T = √(L'/L) = √(1.21) = 1.10. The percentage change is 10%. This uses the binomial/square-root scaling property (NCERT Class 11 Physics, Chapter 13, page 271).

Why A is wrong: A is wrong because 5% comes from dividing the 21% by 4, as if T ∝ L^(1/4); the square root halves a small percentage change, giving about 10% (exactly √1.21 = 1.10).

Why B is wrong: B is wrong because 42% assumes T ∝ L² or doubles the percentage — neither matches the actual square-root dependence.

Why C is wrong: C is wrong because 21% assumes T ∝ L (linear), but T ∝ √L — a 21% increase in L gives only a 10% increase in T (trap: linear scaling instead of square-root).

Answer: A. T = 2π√(L/g_eff). When the lift accelerates upward, g_eff = g + a > g, so √(L/g_eff) < √(L/g), and T decreases (NCERT Class 11 Physics, Chapter 13, page 271).

Why B is wrong: B is wrong because an increase in effective g means the denominator inside the square root increases, making the square root smaller — the period decreases, not increases (trap: confusing the direction of the g_eff effect).

Why C is wrong: C is wrong because this assumes the period is unaffected by the lift's acceleration, but the pseudo-force modifies g_eff, which directly enters the period formula.

Why D is wrong: D is wrong because the effective g is constant as long as the lift has constant upward acceleration — there is no oscillatory behavior in the period itself.