Track OABCD (as shown in figure ) is smooth. What minimum speed has to be given to a particle lying at point A, so that it can reach point C? (take `g=10 m//s^2`)

Options

A. `60 m//s`
B. `100 m//s`
C. `70 m//s`
D. `80 m//s`

Answer

D

Explanation

Maximum tension in the string is in its lowest position.
`h = l (1-costheta_(0))`
Speed of mass m in its lowest position is
`v^(2)=2gh=2gl(1-costheta_(0))`
Now `T_("max")-mg = (mv^(2))/(l)`
or `T_("max") = mg +(mv^(2))/(l) = mg +2mg (1-cos theta_(0))`
or `T_("max")= mg (3-2costheta_(0))`
Block of mass 4m does not move
`therefore " "mu(4mg)geT_("max")`
or `4mu" "mg gemg(3-2costheta_(0))" or "mu ge ((3-2costheta_(0))/(4))`