Two inclined planes are placed as shown in figure. A block is… | JEE Main 2022 (27 Jul, Shift 2)

Q17JEE Main 2022 · 27 JUL · SHIFT 2Difficult

Friction on an Incline

Two inclined planes are placed as shown in figure. A block is projected from the Point A of inclined plane AB along its surface with a velocity just sufficient to carry it to the top Point B at a height 10 m. After reaching the Point B the block slides down on inclined plane BC. Time it takes to reach to the point C from point A is $t(\sqrt{2}+1)$ s. The value of t is ___________.

(use $g = 10\text{ m/s}^{2}$ )

Numerical answer type. Work it out, then open the answer.

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Answer: 2

AB (smooth, $45^\circ$ ): length $= 10\sqrt{2}$ m, retardation $g\sin 45^\circ = 5\sqrt{2}$ m/s $^2$ , and the block just stops at B.
Reverse motion: $t_1 = \sqrt{\frac{2L}{a}} = \sqrt{\frac{2 \times 10\sqrt{2}}{5\sqrt{2}}} = 2$ s
BC ( $30^\circ$ ): length $= \frac{10}{\sin 30^\circ} = 20$ m, $a = g\sin 30^\circ = 5$ m/s $^2$ , starts from rest.
$t_2 = \sqrt{\frac{2 \times 20}{5}} = 2\sqrt{2}$ s
$t_1 + t_2 = 2 + 2\sqrt{2} = 2(\sqrt{2}+1)$ s, so $t = 2$ .

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