A car is moving in a circular horizontal track of radius 10 ~m the...

A car is moving in a circular horizontal track of radius

10 \mathrm{~m}

the roof of the car by a light wire of length

1.0 \mathrm{~m}

. The angle made by the wire with the vertical is: A car is moving in a circular horizontal track of radius 10 ~m the roof of the car by a light wire of length 1.0 ~m .

A car is moving in a circular horizontal track of radius 10 ~m the roof of the car by a light wire of length 1.0 ~m .

Options

A $\frac{\pi}{3}$
B $\frac{\pi}{6}$
C $\frac{\pi}{4}$
D $0^{\circ}$

Correct answer

C. $\frac{\pi}{4}$

Step-by-step solution

From the question

v=10 \mathrm{ m} / \mathrm{s}, \mathrm{r}=10\mathrm{m}, \mathrm{g}=10 \mathrm{ m} / \mathrm{s}^2

\theta=

angle made by wire with vertical then

\begin{aligned} \tan \theta& =\frac{V^2}{r g}\\ & =\frac{10 \times 10}{10 \times 10}=1 \\ \tan \theta=1 \Rightarrow \theta=\tan ^{-1}& (\mathrm{i})=\frac{\pi}{4} \end{aligned}

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