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Question

A block is sliding along inclined plane as shown in figure. If the acceleration of chamber is $$a$$, as shown in the figure. The time required to cover a distance $$L$$ along incline is:

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A
2Lgsinθacosθ
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B
2Lgsinθ+asinθ
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C
2Lgsinθ+acosθ
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D
2Lgsinθ
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Solution

The correct option is B $$\displaystyle \sqrt{\frac{2L}{g\sin \theta +a\cos \theta }}$$
Applying pseudo force $$ma$$ along left direction of the block. 
The net acceleration along the incline will be $$a_{effective}= a \cos \theta+ g \sin \theta$$
The time required will be $$L = 0\times t +\dfrac{1}{2}a_{effective}t^2$$

$$\Rightarrow  \sqrt{\dfrac{2L}{a_{effective}}}$$

$$\Rightarrow  \sqrt{\dfrac{2L}{ a\cos \theta+g \sin \theta}}$$


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Physics

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