A weightless thread can with stand tension upto 30N.A stone of mass 0.5 kg is tied to it and is revolved in a circular path of radius 2 m in a vertical plane. If g=10 `ms^(-2)`, then maximum angular velocity of stone is

Options

A. `4rads^(-1)`
B. `5rads^(-1)`
C. `6rads^(-1)`
D. `7rads^(-1)`

Answer

B

Explanation

Given tension ,T =30 N, mass , m =0.5kg
radius ,r= 2m and g=10`ms^(-2)`
`because` Stone will have maximum velocity at the bottom of the vertical circel.
Maximum angular velocity`omega_(max)=? ``therefore T -mg =(mv_(max)^(2))/(r) or 30-0.5xx10=(0.5v_(max)^(2))/(2)`
`sqrt(25xx4)=v_(max)rArrv_(max)=r(omega_(max))``omega_(max)=(v_(max))/(r)=sqrt(100)/(2)=5rads^(-1)`