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MHT CET 202622 AprilMorning Shift
Exam
MHT CET
Year
2026
Date
22 April
Shift
Morning Shift
Subject
Physics
Chapter
Mathematics in Physics

MHT CET 2026 · 22 April · Morning Shift · Physics · Mathematics in Physics

A student measures times for 20 oscillations of a simple pendulum...

A student measures times for 20 oscillations of a simple pendulum as 30s, 32s, 35s and 31s. If the minimum division in the measuring clock is 1s, then correct mean time in second , within error limits , is

Options

  1. A(32±5)s(32 \pm 5)\text{s}
  2. B(32±3)s(32 \pm 3)\text{s}
  3. C(32±2)s(32 \pm 2)\text{s}
  4. D(32±1)s(32 \pm 1)\text{s}

Correct answer

C. (32±2)s(32 \pm 2)\text{s}

Step-by-step solution

Mean time tmean=30+32+35+314=1284=32 st_{mean} = \dfrac{30 + 32 + 35 + 31}{4} = \dfrac{128}{4} = 32\text{ s}

Absolute errors in each measurement are:
Δt1=∣30−32∣=2 s\Delta t_1 = |30 - 32| = 2\text{ s}
Δt2=∣32−32∣=0 s\Delta t_2 = |32 - 32| = 0\text{ s}
Δt3=∣35−32∣=3 s\Delta t_3 = |35 - 32| = 3\text{ s}
Δt4=∣31−32∣=1 s\Delta t_4 = |31 - 32| = 1\text{ s}

Mean absolute error Δtmean=2+0+3+14=64=1.5 s\Delta t_{mean} = \dfrac{2 + 0 + 3 + 1}{4} = \dfrac{6}{4} = 1.5\text{ s}

Since the minimum division (least count) of the measuring clock is 1 s1\text{ s}, the mean absolute error must be rounded off to the nearest integer to match the precision of the instrument.

Rounding 1.5 s1.5\text{ s} to the nearest integer gives 2 s2\text{ s}.

Therefore, the correct mean time within error limits is (32±2) s(32 \pm 2)\text{ s}.

Answer: (32±2)s(32 \pm 2)\text{s}
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