First slide

Pseudo force

Question

A smooth inclined plane of length l, having an inclination $θ$ with horizontal is inside a lift which is moving down will retardation a. The time taken by a body to slide down the inclined plane from rest will be

Moderate

A

$\sqrt{2 L / (asin θ)}$
B

$\sqrt{2 L / (gsin θ)}$
C

$\sqrt{2 L / (g - a) \sin θ}$
D

$\sqrt{2 L / (g + a) \sin θ}$

Solution

$Using s = ut + \frac{1}{2} {at}^{2}, we have$
$\begin{aligned} L = 0 [\frac{1}{2} (g + a) \sin θ] t^{2} \\ ∴ t = {[\frac{2 L}{(g + a) \sin θ}]}^{1 / 2} \end{aligned}$
On inclined plane, g sin $θ$ is replaced by (g + a) sin $θ$ as the lift is moving down with retardation a (this is equivalent to moving up with acceleration a).

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