JAMB Physics 2019 Paper

Concept:The heat gained by an object is given by $H = mc\theta$, where $m$ is mass, $c$ is specific heat capacity, and $\theta$ is the temperature change.Explanation:Both objects receive the same quantity of heat, so $H_A = H_B$.Using $H = mc\theta$, we write:$$m_A c_A \theta_A = m_B c_B \theta_B$$From the question, $\theta_A = 2\theta_B$ and $m_A = \frac{1}{2}m_B$.Substitute these into the heat equation:$$\left(\frac{1}{2}m_B\right)c_A(2\theta_B) = m_B c_B \theta_B$$Simplify the left-hand side:$$m_B c_A \theta_B = m_B c_B \theta_B$$Cancel the common terms $m_B$ and $\theta_B$ on both sides:$$c_A = c_B$$Therefore, the ratio of specific heat capacity of A to B is:$$\frac{c_A}{c_B} = \frac{1}{1}$$Answer:The ratio is $1 : 1$.Correct option: C.