JEE MAIN - Physics (2019 - 8th April Morning Slot - No. 27)
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Explanation
We know, m = V . $$\rho$$
where, V = volume and $$\rho$$ = density.
So, we have
$${{dQ} \over {dt}} = {h \over {ms}}(T - {T_0}) = {{h(T - {T_0})} \over {V\,.\,\rho s}}$$
Since, h, (T $$-$$ T0) and V are constant for both beaker.
$$\therefore$$ $${{dQ} \over {dt}} \propto {1 \over {\rho s}}$$
We have given that $$\rho$$A = 8 $$\times$$ 102 kgm$$-$$3, $$\rho$$B = 103 kgm$$-$$3, sA = 2000 J kg$$-$$1 K$$-$$1 and sB = 4000 J kg$$-$$1 K$$-$$1, $$\rho$$AsA = 16 $$\times$$ 105 and $$\rho$$BsB = 4 $$\times$$ 106
$$\rho$$A < $$\rho$$B, sA < sB and $$\rho$$AsA < $$\rho$$BsB
$$ \Rightarrow {1 \over {{\rho _A}{s_A}}} > {1 \over {{\rho _B}{s_B}}} \Rightarrow {{d{Q_A}} \over {dt}} > {{d{Q_B}} \over {dt}}$$
So, for container B, rate of cooling is smaller than the container A. Hence, graph of B lies above the graph of A and it is not a straight line (slope of A is greater than B).
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