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Question

A bead starts sliding from a point P on a frictionless wire with initial velocity of 5 $$ms^{-1}$$. Find the velocity of bead at point R (take g = 10 $$ms^{-2}$$)
1565036_31b530b1e6144e14aeeb73f858722bb1.GIF


A
7 m/s
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B
105 m/s
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C
62 m/s
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D
6 m/s
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Solution

The correct option is C $$6\sqrt 2$$ m/s
$$\begin{array}{l}\text { Given-* Initial velocity of the Bead } v_{0}=5 \mathrm{~m} / \mathrm{s} \\\text { By conservation of energy- } \\\text { Total Energy at point } p=\text { Total Energy at point } R \\\Rightarrow p E_{p}+k E_{p}=p E_{R}+k E_{R} \\\Rightarrow m g h_{p}+\frac{1}{2} m v_{0}^{2}=m g h_{R}+\frac{1}{2} m v_{R}^{2}\end{array} $$
$$\begin{array}{l}\Rightarrow g\cdot(4)+\frac{v_{0}^{2}}{2}=g\cdot(1\cdot 65)+\frac{v_{R}^{2}}{2} \\\Rightarrow v_{R}^{2}=72 \\\Rightarrow v_{R}=\sqrt{72} m / 8=6 \sqrt{2} \mathrm{~m} / \mathrm{s} \\\text { Hence, option (c) is correct. }\end{array}$$

Physics

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