A simple pendulum, a bob of mass 0.20 kg on a light string 0.80 m long, hangs from the roof of a…

Step 1. Angle (a). $\tan\theta = \dfrac{a}{g} = \dfrac{7.5\ \text{m/s}^2}{10\ \text{m/s}^2}$, so $\theta = 36.9^\circ$, the bob trailing behind.

Step 2. Period in the car (b). $g_{\text{eff}} = \sqrt{g^2 + a^2} = 12.5\ \text{m/s}^2$, so

Step 3. Tension (c). At rest in the car the string balances the effective weight: $T_s = m g_{\text{eff}} = 0.20\ \text{kg} \times 12.5\ \text{m/s}^2 = 2.50\ \text{N}$.

Step 4. In the lift (d). The lift accelerates downwards at $2.5\ \text{m/s}^2$, so $g_{\text{eff}} = 10\ \text{m/s}^2 - 2.5\ \text{m/s}^2 = 7.5\ \text{m/s}^2$ and $T = 2\pi\sqrt{0.80\ \text{m} / 7.5\ \text{m/s}^2} = 2.05\ \text{s}$.