A small block of mass m , charge +q is kept at the top of a smooth inclined plane of angle 30° placed in an elevator moving upward with an acceleration a0 . Electric field E exists between the vertical side walls of the elevator. The time taken by the block to come to the lowest point of inclined plane is (assuming the surface to be smooth)

t = 2 2 h ( g + a 0 ) − 3 q E m

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A small block of mass m , charge +q is kept at the top of a smooth inclined plane of angle $30 °$ placed in an elevator moving upward with an acceleration a₀ . Electric field E exists between the vertical side walls of the elevator. The time taken by the block to come to the lowest point of inclined plane is (assuming the surface to be smooth)

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$t = 2 \sqrt{\frac{2 h}{(g + a_{0}) - \frac{\sqrt{3} q E}{m}}}$

$t = \sqrt{\frac{2 h}{(g - a_{0}) + \frac{q E}{m}}}$

$\sqrt{\frac{2 h}{(g + a)^{2} - (\frac{qE}{m}) h^{2}}}$

$t = \sqrt{\frac{2 h}{g}}$

answer is C.

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Net acc of block down the incline is

$a = \frac{(g + a_{0})}{2} - \frac{\sqrt{3} q E}{2 m} \Rightarrow a = \frac{1}{2} (g + a_{0} - \frac{\sqrt{3} q E}{m})$

Now $\frac{h}{\sin 30} = \frac{1}{2} a t^{2}$

$\Rightarrow 2 h = \frac{1}{4} [g + a_{0} - \sqrt{3} (\frac{q E}{m})] t^{2}$

$\Rightarrow t = \sqrt{\frac{8 h}{g + a_{0} - \sqrt{3} (\frac{q E}{m})}}$

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