Question 117: Work, Energy and Power & Circular Motion

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 angle of 45$$^\circ$$, 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.

Accepted Answer

On a horizontal ground,
$${v_{\max }} = \sqrt {\mu Rg}  = \sqrt {0.2 	imes 2 	imes 9.8}  = 1.97$$ m/s
= $$1.97 	imes {{18} \over 5}$$
= 7.12 km/hr = 7.2 km/hr
Statement - 2
$${v_{\max }} = \sqrt {gr\left( {{{	an 	heta  + \mu } \over {1 - \mu 	an 	heta }}} ight)}  = \sqrt {2 	imes 9.8 	imes {{12} \over {0.8}}}  = 19.5$$ km/hr
$${v_{\min }} = \sqrt {rg\left( {{{	an 	heta  - \mu } \over {1 + \mu 	an 	heta }}} ight)}  = \sqrt {2 	imes 9.8 	imes {{0.8} \over {1.2}}}  = 12.01$$ km/hr

Answer

Statement I is incorrect and statement II is correct

Answer

Both statement I and statement II are true

Answer

Statement I is correct and statement II is incorrect

Answer

Both statement I and statement II are false

Work, Energy and Power & Circular Motion

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