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Physics-

General

Easy

Question

Radius of the curved road on national highway is $R.$ Width of the road is $b.$ The outer edge of the road is raised by $h$ with respect to inner edge so that a car with velocity $v$ can pass safe over it. The value of $h$ is

$\frac{v^{2} b}{R g}$
$\frac{v}{R g b}$
$\frac{v^{2} R}{g}$
$\frac{v^{2} b}{R}$

The correct answer is: $fraction numerator v to the power of 2 end exponent b over denominator R g end fraction$

We know that $tan invisible function application theta equals fraction numerator v to the power of 2 end exponent over denominator R g end fraction$ and $tan theta equals invisible function application fraction numerator h over denominator b end fraction$
Hence $fraction numerator h over denominator b end fraction equals fraction numerator v to the power of 2 end exponent over denominator R g end fraction rightwards double arrow h equals fraction numerator v to the power of 2 end exponent b over denominator R g blank end fraction$

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A frictionless track $A B C D E$ ends in a circular loop of radius $R comma$ figure. A body slides down the track from point $A$ which is at a height $h equals 5 blank$ cm. Maximum value of $R$ for the body to successfully complete the loop is
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$A blank p a r t i c l e blank o f blank m a s s blank m blank i s blank m o v i n g blank i n blank a blank h o r i z o n t a l blank c i r c l e blank o f blank r a d i u s blank r comma blank u n d e r blank a blank c e n t r i p e t a l blank f o r c e$
$equals fraction numerator k over denominator r to the power of 2 end exponent ´ end fraction w h e r e blank k blank i s blank a blank c o n s t a n t.$

$A blank p a r t i c l e blank o f blank m a s s blank m blank i s blank m o v i n g blank i n blank a blank h o r i z o n t a l blank c i r c l e blank o f blank r a d i u s blank r comma blank u n d e r blank a blank c e n t r i p e t a l blank f o r c e$
$equals fraction numerator k over denominator r to the power of 2 end exponent ´ end fraction w h e r e blank k blank i s blank a blank c o n s t a n t.$

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