A vehicle of mass `m` is moving on a rough horizontal road with momentum `P` . If the coefficient of friction between the tyres and the road be `mu`, then the stopping distance is:

Options

A. `p/(2 mumg)`
B. `(p^(2))/(2mumg)`
C. `p/(2mum^(2)g)`
D. `(p^(2))/(2mum^(2)g)`

Answer

D

Explanation

Initial K.E=`1/2mv^2=E`
Final K.E=`1/2m(v/2)^2=1/2m*(v^2)/(4)`
`=1/4(1/2mv^2)=E/4`
`:.` Loss is K.E=E-`E/4=3/4E`
This energy is used in doing work in penetrating the block. If the retarding force in uniform, then`Wprops` and `WpropE`
`:." "spropE`
Thus for `(3E)/4` it penetrates through 3cm
`:.` For the remaining `1/4E`, it will penetrate a further distance of 1cm.