Which driving a car around a curve of 200 m radius ,the driver notices that a simple rendulum hung to the roof of the car is marking an angle of `15^(@)` to the horizontal ,what is the speed of the car km /h ?
`(g=10m//s^(2))("use " tan 15^(@)=0.2645)`

Options

A. 75
B. 83
C. 91
D. 98

Answer

B

Explanation

For equilibrium ` tan theta = (v^(2))/(r g )`
` therefore v^(2) = rg tan theta = 200xx10xx tan 15^(@)`
`=2000xx0.2645 = 529`
` therefore v= sqrt( 529)= 23 m// s `
` therefore v= 23 xx(18)/(5) km //h underset(*)overset(*)= 83 km //h`
`[ :' 1 km //h =(5)/(18) m//s " " therefore 1m//s =(18)/(5) km//h]`