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If the ratio of densities of two substances is $5: 6$ and the ratio of their specific heat capacities is $3: 5$, then the ratio of heat energies required per unit volume so that the two substances can have same temperature rise is
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The correct answer is:
1:2
Ratio of densities of two substance, $\frac{\mathrm{d}_1}{\mathrm{~d}_2}=\frac{5}{6}$
Ratio of their specific heat capacities, $\frac{c_1}{c_2}=\frac{3}{5}$
$$
\begin{aligned}
& \Delta Q=m c \Delta T=d c \Delta T \\
& \Delta Q_1=d_1 c_1 \Delta T \\
& \Delta Q_2=d_2 c_2 \Delta T \\
& \frac{\Delta Q_1}{\Delta Q_2}=\frac{d_1 c_1}{d_2 c_2}=\frac{5}{6} \times \frac{3}{5}=\frac{1}{2}
\end{aligned}
$$
Ratio of their specific heat capacities, $\frac{c_1}{c_2}=\frac{3}{5}$
$$
\begin{aligned}
& \Delta Q=m c \Delta T=d c \Delta T \\
& \Delta Q_1=d_1 c_1 \Delta T \\
& \Delta Q_2=d_2 c_2 \Delta T \\
& \frac{\Delta Q_1}{\Delta Q_2}=\frac{d_1 c_1}{d_2 c_2}=\frac{5}{6} \times \frac{3}{5}=\frac{1}{2}
\end{aligned}
$$
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