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STD 11 - 4.1. newtons laws of motion — NEET STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceNEETSTD 11 - 4.1. newtons laws of motion4 Marks
Question
A wedge of height $H$ (fixed) and inclination $\alpha $ (variable) is moving on a smooth horizontal surface with constant acceleration $g\ m/s^2$ . A small block is placed at bottom of incline as shown in figure, slips on the smooth surface of incline . Choose $CORRECT$ statement about time taken by block to reach the top of incline
✓

Answer

Acceleration up to incline

$a=g \cos \alpha-g \sin \alpha$

time to reach top

$\frac{\mathrm{H}}{\sin \alpha}=\frac{1}{2}(g)(\cos \alpha-\sin \alpha) \mathrm{t}^{2}$

$t^{2}=\frac{2 H}{g}=\frac{1}{\sin \alpha \cos \alpha-\cos ^{2} \alpha}$

$=\frac{4 \mathrm{H}}{\mathrm{g}} \frac{1}{\sin 2 \alpha-1+\cos ^{2} \alpha}$

$=\frac{4 \mathrm{H}}{\mathrm{g}} \frac{1}{\left(\sin 2 \alpha+\cos ^{2} \alpha\right)-1}$

so $t$ first decreases than increases.

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