Question

In shown figure a triangular wedge and a cylinder each having equal mass m are released from rest. The vertical wall and horizontal surface are frictionless and between the wedge and the cylinder friction is sufficient to allow cylinder to roll over it choose correct option(s)
A. Acceleration of wedge is `(g)/(3)`
B. Minimum value of coefficient of friction between wedge and cylinder without slipping is `(1)/(3)`
C. minimum value of coefficient of friction between wedge an cylinder for rolling without slipping is `(1)/(2)`
D. if `m=3sqrt(20)kg`, the contact force between cylinder and wedge is 100 N.

Answer 1

Correct Answer - A::B::D

`mg-f_(s)sin45^(@)-N_(1)cos45^(@)=ma_(1)` .(1)
`f_(s)R=(mR^(2))/(2)alpha` ..(2)

`N_(1)sin45^(@)-f_(s)cos45^(@)=ma_(2)` .(3)
for rolling
`Ralpha-a_(a)sin45^(@)=a_(2)cos45^(@)` .(4)
`mu_(min)=(f_(S))/(N_(1))`
contact force `F=sqrt(N_(1)^(2)+f_(S)^(2))`