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A circular road of $1000 \mathrm{~m}$ radius has banking angle $45^{\circ}$, the maximum safe speed of a car having 2000 $\mathrm{kg}$. mass will be, if the coefficient of friction between tyre and road is 0.5 .
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Verified Answer
The correct answer is:
$172 \mathrm{~m} / \mathrm{sec}$
$172 \mathrm{~m} / \mathrm{sec}$
Given that $r=1000 \mathrm{~m} ; \theta=45^{\circ}$; and $\mu=0.5$;
Maximum safe velocity:
$\begin{aligned} & v=\sqrt{\frac{r g(\tan \theta+\mu)}{1-\mu \tan \theta}} \\ & v=\sqrt{\frac{1000 \times 9.8\left(\tan 45^{\circ}+0.5\right)}{1-0.5 \times \tan 45^{\circ}}}\end{aligned}$
$v=172 \mathrm{~m} / \mathrm{s}$
So the correct answer is option 4.
Given that $r=1000 \mathrm{~m} ; \theta=45^{\circ}$; and $\mu=0.5$;
Maximum safe velocity:
$\begin{aligned} & v=\sqrt{\frac{r g(\tan \theta+\mu)}{1-\mu \tan \theta}} \\ & v=\sqrt{\frac{1000 \times 9.8\left(\tan 45^{\circ}+0.5\right)}{1-0.5 \times \tan 45^{\circ}}}\end{aligned}$
$v=172 \mathrm{~m} / \mathrm{s}$
So the correct answer is option 4.
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