# 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

As we learnt in

Time period of oscillation of simple pendulum -

- wherein

l = length of pendulum

g = acceleration due to gravity.

Times lost / gained per day

Where Co-efficient of linear expansion.

(i)

(ii)

On dividing we get

After put the value of  we get

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.

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