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A simple pendulum is set up in a trolley which moves to the right with an acceleration a on a horizontal plane. Then the thread of the pendulum in the mean position makes an angle $\mathrm{\theta }$ with the vertical

(a) ${\mathrm{tan}}^{-1}\left(\frac{\mathrm{a}}{\mathrm{g}}\right)$ in the forward direction

(b) ${\mathrm{tan}}^{-1}\left(\frac{\mathrm{a}}{\mathrm{g}}\right)$ in the upward direction

(c) ${\mathrm{tan}}^{-1}\left(\frac{\mathrm{a}}{\mathrm{g}}\right)$ in the backward direction

(d) ${\mathrm{tan}}^{-1}\left(\frac{g}{a}\right)$ in the forward directions