Question

A solid cylinder of mass `m` is kept in balance on a fixed incline of angle `alpha=37^@` with the help of a thread fastened to its jacket. The cylinder does not slip.

In what direction should the thread be pulled to minimise the force required to hold the cylinder? What is the magnitude of this force?
A. `3mg//10` parallel to incline
B. vertical `3mg//8`
C. horizontal `mg//5`
D. `3mg//5` perpendicular to incline

Answer 1

Correct Answer - A
Let force is applied at angle `theta` as shown with incline again `f=F`
`Fcostheta+f=mgsinalpha`
`impliesFcostheta+F=(3mg)/5`

`implies F=(3mg)/(5(1+costheta))`
`F` is minimum when `costheta=1`
`impliestheta=0^@`
`implies F_(min)=(3mg)/(5[1+1])=(3mg)/10`