Time period of simple pendulum at a planet is 2 sec. Length of simple pendulum is 2 meter. Find the value of g at that planet (in m/s^{2})

(1) 2$\pi$^{2}

(2) 9.8 m/s^{2}

(3) 10 m/s^{2}

(4) $\pi^2\over2$m/s^{2}

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Ans. (1) 2$\pi$^{2}

Sol. $T=2\pi\sqrt{\ell\over g_\text{planet}}$

$\implies2=2\pi\sqrt{2\over g_\text{planet}}$

$\implies{1\over\pi^2}={2\over g_\text{planet}}$

$\implies$ g_{planet} = 2$\pi$^{2} m/sec^{2}

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