JEE MAIN - Physics (2019 - 11th January Evening Slot - No. 25)
Two rods A and B of identical dimensions are at temperature 30°C. If A is heated upto 180oC and B upto ToC, then the new lengths are the same. If the ratio of the coefficients of linear expansion of A and B is 4 : 3, then the value of T is
200oC
270oC
230oC
250oC
Explanation
$$\Delta {\ell _1} = \Delta {\ell _2}$$
$$\ell {\alpha _1}\Delta {T_1} = \ell {\alpha _2}\Delta {T_2}$$
$${{{\alpha _1}} \over {{\alpha _2}}} = {{\Delta {T_1}} \over {\Delta {T_2}}}$$
$${4 \over 3} = {{T - 30} \over {180 - 30}}$$
$$T = {230^o}C$$
$$\ell {\alpha _1}\Delta {T_1} = \ell {\alpha _2}\Delta {T_2}$$
$${{{\alpha _1}} \over {{\alpha _2}}} = {{\Delta {T_1}} \over {\Delta {T_2}}}$$
$${4 \over 3} = {{T - 30} \over {180 - 30}}$$
$$T = {230^o}C$$
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