A clock pendulum made of invar has a period of $0.5$ sec at$20^{\circ}$. If the clock is used in a climate where the temperature averages to $30^{\circ}C,$ how much time does the clock lose in each oscillation? (for invar, $\alpha=9 \times 10^{-7}/^{\circ}C,g= constant )$

Question

\[\begin {array} {1 1} (1)\;2.25 \times 10^{-6}\;sec & \quad (2)\;2.5 \times 10^{-7}\;sec \\ (3)\;5 \times 10^{-7}\;sec & \quad (4)\;1.125 \times 10^{-6}\;sec \end {array}\]