Question

A body is moving is down an inclined plane of slope `37^@` the coefficient of friction between the body and the plane varies as `mu=0.3x`, where x is the distance traveled down the plane by the body. The body will have maximum speed. `(sin 37^@ =(3)/(5))` .
A. at `x= 1.16 m`
B. at `x= 2m`
C. at bottommost point of the plane
D. at `x = 2.5 m`

Answer 1

Correct Answer - D
`F("net") =mg sin theta -mu ng cos theta`
`=mg sin theta-0.3 xmg cos theta`…. (i)
At maximum speed `F_("net") =0`. Because after this net force Eq.(i), `F_("net") =0` at
`x=(tantheta)/(0.3) =(3/4)/(0.3) =2.5 m`