A boy of mass 30 kg starts running from rest along a circular path of radius 6 m with constant tangential acceleration of magnitude `2 m s^(-2)`. After 2 s from start he feels that his shoes started slipping on th ground. The friction between his shoes and ground is
(Take `g=10 m s^(-2)`)

Options

A. `(1)/(2)`
B. `(1)/(3)`
C. `(1)/(4)`
D. `(1)/(5)`

Answer

B

Explanation

After `2 sec` speed of boy will be
`v=2xx2=4m//s`
At this moment centripetal force on boy is
`F_(r)=(mv^(2))/(R)=(30xx16)/(6)=80Nt. `
Tangential forc on boy is
`F_(t)=ma=30xx2=60Nt.`
Total friction acting on boy is
`F=sqrt(F_(r)^(2)+F_(t)^(2))=100Nt`
At the time of slipping
`F=mumg`
or `100 =mu xx 30 xx 10`
`rArr mu=(1)/(3)`