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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Physics
Chapter
Thermal Properties of Matter

NTA Abhyas 2020 · Physics · Thermal Properties of Matter

A clock that keeps correct time at 20 ° C , is subjected to 40 ° C...

A clock that keeps correct time at 20°C20 ° C, is subjected to 40°C40 ° C. If the coefficient of linear expansion of the pendulum is 12×10−6°C−112 \times {10}^{- 6} ° C^{- 1}, the time gained or lost, per day, is

Options

  1. A10.3sday−110.3s{day}^{- 1}
  2. B20.6sday−1{20.6sday}^{- 1}
  3. C5sday−1{5sday}^{- 1}
  4. D20minday−1{20min day}^{- 1}

Correct answer

A. 10.3sday−110.3s{day}^{- 1}

Step-by-step solution

Time period, T=2πlgT = 2\pi\sqrt{\dfrac{l}{g}}

∆TT=12∆ll=12α∆θ\dfrac{∆ T}{T} = \dfrac{1}{2}\dfrac{∆ l}{l} = \dfrac{1}{2}\alpha ∆ \theta

=12×12×10−6×(40−20)=12×10−5= \dfrac{1}{2} \times 12 \times {10}^{- 6} \times ( 40 - 20 ) = 12 \times {10}^{- 5}

∆T=T×12×10−5∆ T = T \times 12 \times {10}^{- 5}

= 24×60×60×12×10−524 \times 60 \times 60 \times 12 \times {10}^{- 5}

= 10.3\text{s}{\text{day}^{- 1}
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