Two simple pendulum with heavy bobs-one using iron wire and the other aluminimum wire are excited simultaneously. It is found that when the first pendulum completes 1000 oscillations the other completes 1001. When the temperature is raised by `t^(@)C`, it is found that the two pendulums now oscillate together. If he coefficients of thermal expansion of iron and aluminimum are `10 xx 10^(-6)//^(@)C` and `30 xx 10^(-6)//^(@)C` then the value of t is :

Options

A. `77.2^(@)C`
B. `123.2^(@)C`
C. `100.1^(@)C`
D. `105.2^(@)C`

Answer

C

Explanation

At lower temperature let the time period of the two pendulums be `T_(1)` & `T_(2)`
`1000 T_(1)=1001 T_(2)`
or `1000 sqrt(l)=1001 sqrt(l_(2))`
At higher temp
`l_(1)(1+alpha_(1)t)=l_(2)(1+alpha_(2)t)`
`(l_(1))/(l_(2))=(1+alpha_(2)t)/(1+alpha_(1)t)`
`:. ((1001)/(1000))^(2)=(1_30 xx10^(-6)t)/(1+10 xx10^(-6)t)rArr t = 100.1^(@)C`.