$$Statement-I$$ : A Cyclist is moving on an unbanked road with a speed of $$7$$ $$kmh-1$$ and takes a sharp circular turn along a path of radius of $$2m$$ without reducing the speed. The static friction coefficient is $$0.2$$ the cyclist will not slip and pass the curve $$(g=9.8$$ $$m/s2)Statement-II$$: If the road is banked at an angled of $$450$$, cyclist can cross the curve of $$2m$$ radius with the speed of $$18.5$$ $$kmh-1$$ without slipping.In the light of the above statements, choose the correct answer from the options given below.

Question

$$Statement-I$$ : A Cyclist is moving on an unbanked road with a speed of $$7$$ $$kmh-1$$  and takes a sharp circular turn along a path of radius of $$2m$$ without reducing the speed. The static friction coefficient is $$0.2$$ the cyclist will not slip and pass the curve $$(g=9.8$$ $$m/s2)Statement-II$$: If the road is banked at an angled of $$450$$, cyclist can cross the curve of $$2m$$ radius with the speed of $$18.5$$ $$kmh-1$$ without slipping.In the light of the above statements, choose the correct answer from the options  given below.

Infinity Learn · Accepted Answer

On a horizontal ground $$vmax=$$μ$$Rg=0.2$$×$$2$$×$$9.8=1.97m/s=1.97$$×$$185=7.12km/hrSince$$, cyclist is riding at safer speed of $$7$$ $$km/hr$$,Statement I is correct.Statement $$-2vmax=rgtan$$θ$$+$$μ$$1$$−μ$$tan$$θ$$=2$$×$$9.8$$×$$1.20.8=5.422m/s=19.5$$  $$km/hrvmin=rgtan$$θ−μ$$1+$$μ$$tan$$θ$$=2$$×$$9.8$$×$$0.81.2=3.615m/s=13.01$$ $$km/hrSince$$, speed of cyclist is between the safe limit of vmin and vmax,  Statement II is also correct.

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