A pendulum of mass m hangs from a support fixed to a trolley. The direction of the string (i . e ., angle θ ) when the trolley rolls up a plane of inclination α with acceleration ‘a’ is

# A pendulum of mass m hangs from a support fixed to a trolley. The direction of the string (i . e ., angle $\mathrm{\theta }$ ) when the trolley rolls up a plane of inclination $\mathrm{\alpha }$ with acceleration 'a' is

1. A

Zero

2. B

3. C

4. D

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

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### Solution:

$\mathrm{Tsin\theta }=\mathrm{ma}+\mathrm{mgsin\alpha }...\left(\mathrm{i}\right)$

$\mathrm{Tcos\theta }=\mathrm{mgcos\alpha }...\left(\mathrm{ii}\right)$

$\mathrm{tan\theta }=\left(\frac{\mathrm{\alpha }+\mathrm{gsin\alpha }}{\mathrm{gcos\alpha }}\right)$

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