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On a dry road the maximum safe speed ...

On a dry road the maximum safe speed for a vehicle moving on a curved raod is 30 km/ hour , After heavy showers , the maximum safe speed for the same raod was 18 km/ hour . The ratio of the coefficient of friction for the dry road to that of wett road is

A

`(5)/(3)`

B

`(25)/(9)`

C

`(3)/(5)`

D

`(5)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
`v_(1) = 30 km // hour =30 xx(5) /( 18 ) =(25) /(3) m//s `
` and v_(2) = 18 ` km / hour `= 18xx(5) /( 18) = 5 m//s`
when the vehicle takes a turn , the C.F force `(mv^(2))/( r ) ` is
opposed by the force of friction `F= mu R =mu m g `
` therefore ` for equilibrium `mu mg =(mv^(2) )/(r ) therefore mu = ( v^(2))/( rg) `
In this case ,` ( mu _("Dry"))/(mu _("Wet"))=(V_(1)^(2))/( rg) xx(rg) /( v_(1) ^(2))=(V_(1)^(2))/( v_(2)^(2))`
` therefore (mu _(D ))/( mu _(W )) = ( 25 )/( 3) xx(25) /( 3) xx(1)/(25) = (25) / (9) `
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