A 1 kg stone at the end of 1 m long string is whirled in a vertical circle at constant speed of 4 m/sec. The tension in the string is 6 N when the stone is at `(g =10m//sec^(2))`

Options

A. (a) `10ms^-1`
B. (b) `5sqrt3ms^-1`
C. (c) `10sqrt3ms^-1`
D. (d) `20ms^-1`

Answer

A

Explanation

`m=1kgimpliesL=10/3m`
`(T_(max))/(T_(min))=4` (i)
and `V_L=sqrt(V_H^2+4gL)`
Tension at highest point, `T_(min)=(mv_H^2)/(K)-mg`
Tension at lowest point,
`T_(max)=mv_L^2//L+mg=(m(v_H^2+4gL))/(L)+mg`
Now Eq. (i) can be written as
`m[(v_H^2+4gL)/(L)+g]=4xxm((v_H^2)/(L)-g)`
`implies v_H=sqrt(3gL)=10ms^-1`