A cyclist is moving in a circular track of radius 80 m with a velocity v = 36 km/h . He has to lean from the vertical approximately through an angle: (Take g=10 text ms-2)

Question

A cyclist is moving in a circular track of radius 80 m with a velocity v = 36 km/h . He has to lean from the vertical approximately through an angle: (Take g=10 text ms-2)  (A)  tan -1(4)  (B)  tan -1( (1/3) )  (C)  tan -1( (1/4) )  (D)  tan -1(2)

Tardigrade Admin · Accepted Answer

tan θ =(v2/rg) ⇒ θ = tan -1( (10× 10/80× 10) ) ( ∵ v=36× (5/18)=10 m/s ) = tan -1( (1/8) )

Q. A cyclist is moving in a circular track of radius $80 m$ with a velocity $v = 36 km / h$ . He has to lean from the vertical approximately through an angle: (Take $g = 10 m s^{- 2})$

$tan^{- 1} (4)$

$tan^{- 1} (\frac{1}{3})$

$tan^{- 1} (\frac{1}{4})$

$tan^{- 1} (2)$

$tan^{- 1} (\frac{1}{8})$

$tan θ = \frac{v ^{2}}{r g}$
$\Rightarrow$ $θ = tan^{- 1} (\frac{10 \times 10}{80 \times 10})$
$(∵ v = 36 \times \frac{5}{18} = 10 m / s)$
$= tan^{- 1} (\frac{1}{8})$

Q. A cyclist is moving in a circular track of radius 80m with a velocity v=36km/h . He has to lean from the vertical approximately through an angle: (Take g=10ms−2)

tan−1(4)

tan−1(31​)

tan−1(41​)

tan−1(2)

tan−1(81​)

tanθ=rgv2​ ⇒ θ=tan−1(80×1010×10​) (∵v=36×185​=10m/s) =tan−1(81​)