Question

Assertion(A): In a grid pendulum, there are 3 iron rods and 4 brass rods. Length of each brass rod is $50cm$. $\alpha$ of iron is $12\times {10}^{-6}{/}^{o}C$ and $\alpha$ of brass is $18\times {10}^{-6}{/}^{o}C$. Length of each iron rod is $50cm.$

Reason(R): for grid iron pendulum $n_1{l}_1{\alpha }_1+n_2{l}_2{\alpha }_2=1$

• A. A and R are correct and R is correct explanation for A
• B. A and R are correct and R is not correct explanation for A
• C. A is true and R is false
• D. A is wrong and R is true

Answer 1

The correct option is C A is true and R is false

In a gridiron pendulum, the effective length of the pendulum and hence its time constant does not change with temperature because the expansion of one portion is counterbalanced by the expansion of the other. Hence,

$n_1\Delta l_1=n_2\Delta l_2$

$n_1{l}_1{\alpha }_1=n_2{l}_2{\alpha }_2$

Thus, R is incorrect.

Answer is option C.