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  • Help me answer: A pendulum clock loses 12 s a day if the temperature is 400C and gains 4 s a day if the temperature is 200C. The temperature at which the clock will show correct time, and the co-efficient of linear expansion (α) of the metal of

A pendulum clock loses 12 s a day if the temperature is 400C and gains 4 s a day if the temperature is 200C.  The temperature at which the clock will show correct time, and  the co-efficient of linear expansion (α) of the metal of the pendulum shaft are respectively :

  • Option 1)

     250C;  α = 1.85×10−5/0C

     

  • Option 2)

     600C; α =1.85×10−4/0C

     

  • Option 3)

     300C; α=1.85×10−3/0C

     

  • Option 4)

     550C;  α = 1.85×10−2/0C

 

Answers (1)

best_answer

As we learnt in

Time period of oscillation of simple pendulum -

T=2\pi \sqrt{\frac{l}{g}}

- wherein

l = length of pendulum 

g = acceleration due to gravity.

 

 Times lost / gained per day =\frac{1}{2}\times \alpha\times \Delta\theta\times 86,400\ sin\theta

Where \alpha-Co-efficient of linear expansion.

12=\frac{1}{2}\times(40-\theta)\times 86400                (i)

4=\frac{1}{2}\times(\theta-20)\times 86400                (ii)

On dividing we get

3=\frac{40-theta}{\theta-20}=3\theta-60=40\theta

\therefore\ \; 4\theta=100\ \; \Rightarrow\ \; \theta=25^{o}C

After put the value of \theta we get \alpha

\alpha=1.85\times 10^{-5}

Correct option is 1.


Option 1)

 250C;  α = 1.85×10−5/0C

 

This is the correct option.

Option 2)

 600C; α =1.85×10−4/0C

 

This is an incorrect option.

Option 3)

 300C; α=1.85×10−3/0C

 

This is an incorrect option.

Option 4)

 550C;  α = 1.85×10−2/0C

This is an incorrect option.

Posted by

divya.saini

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