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Motion in a Straight Line — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsMotion in a Straight Line2 Marks
Question
Points P, Q and R are in a vertical line such that PQ = QR. A ball at P is allowed to fall freely. What is the ratio of the times of descent through PQ and QR?
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Answer

Let t, and tą be the times of descent through PQ and QR, respectively. Let PQ = QR = h Then, $\text{h}=\frac{1}{2}\text{gt}^2_1$ and $2\text{h}=\frac{1}{2}\text{g}(\text{t}_1+\text{t}_2)^2$ By dividing, we get $\frac{1}{2}=\frac{\text{t}^2_1}{(\text{t}_1+\text{t}_2)^2}$ $\frac{1}{\sqrt{2}}=\frac{\text{t}_1}{\text{t}_1+\text{t}_2}$ Hence, $\text{t}_1:\text{t}_2=2:(\sqrt{2}-1)$

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