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The figure shows a cart moving up with acceleration a along an incline of inclination a.
A pendulum hanging in equilibrium inside the car makes angle $θ$ with the normal to the incline. The value of $\tan θ$ is.

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$\frac{g \sin α + a}{g \cos α}$

$\frac{g \sin α}{a}$

$\frac{a}{g \cos α}$

$\frac{g \cos α - a}{g \sin α}$

answer is A.

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Detailed Solution

The figure shows the forces acting on the pendulum. Using dynamics along the incline and perpendicular to the incline, we have

$T \sin θ - m g \sin α = m a T \cos θ = m g \cos α$

Eliminating T we have

$\tan θ = \frac{g \sin α + a}{g \cos α}$

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