Question

Statement I : A cyclist is moving on an unbanked road with a speed of $7km{h}^{-1}$ and takes a sharp circular turn along a path of radius of $2m$ without reducing the speed. The static friction coefficient is $\mathrm{0.2.}$ The cyclist will not slip and pass the curve $\left(g=9.8m/s^2\right)$
Statement II : If the road is banked at an angle of $45^{\circ }$, cyclist can cross the curve of $2m$ radius with the speed of $18.5km{h}^{-1}$ without slipping.
In the light of the above statements,
choose the correct answer from the options given below.

• A. Statement I is incorrect and statement II is correct
• B. Statement I is correct and statement II is incorrect
• C. Both statement I and statement II are false
• D. Both statement I and statement II are true

Answer 1

Answer: (D)

Statement I :
$v_{\max }=\sqrt{\mu Rg}=\sqrt{(0.2)\times 2\times 9.8}$
$v_{\max }=1.97m/s$
$7km/h=1.944m/s$
Speed is lower than $v_{\max }$, hence it can take safe turn.
Statement II
$v_{\max }=\sqrt{\mathrm{Rg}\left[\frac{\tan \theta +\mu }{1-\mu \tan \theta }\right]}$
$=\sqrt{2\times 9.8\left[\frac{1+0.2}{1-0.2}\right]}=5.42m/s$
$18.5km/h=5.14m/s$
Speed is lower than $v_{\max }$, hence it can take safe turn.