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  • A uniform rod of length 30cm is lying on a horizontal plane. If its opposite ends are moving with speed 1m/s and 2m/s respectively in the opposite directions. Then the instantaneous axis of rotatio

A uniform rod of length 30cm is lying on a horizontal plane. If its opposite ends are moving with speed 1m/s and 2m/s respectively in the opposite directions. Then the instantaneous axis of rotation will be at a distance of xcm from the axis of rotation of its right end, moving with a speed of 2m/s. Then \frac{x}{l} will be

 

Option: 1

\frac{1}{3}


Option: 2

\frac{2}{3}


Option: 3

\frac{1}{2}


Option: 4

\frac{3}{4}


Answers (1)

best_answer

\tan \theta=\frac{1}{(l-x)}=\frac{2}{x}

\begin{aligned} & x=2 l-2 x \\ & 3 x=2 l \\ & x=\frac{2 l}{3} \\ & x=\frac{2}{3} \times 36 \mathrm{~cm} \\ & x=20 \mathrm{~cm} \end{aligned}

\text { so, } \frac{x}{l}=\frac{20 \mathrm{~cm}}{30 \mathrm{~cm}}=\frac{2}{3}

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Riya

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