A string of length `0.5` m is suspended from a ceiling and holds a sphere of mass `0.2 ` kg . The sphere is made to describes a horizontal circle of radius of radius `0.3` m . The speed of the sphere will be

Options

A. `1.5 ms^(-1)`
B. `2.0 ms^(-1)`
C. `2.5 ms^(-1)`
D. `3.0 ms^(-1)`

Answer

A

Explanation

Given l = 0.5 m , m = 0.2 kg , r = 0.3 m , `g = 10 m//s^(2), mg = S cos theta `
or `(mv^(2))/R xx 1/(mg) =(S sin theta)/(S cos theta) = tan theta or v^(2) =Rg tan theta `
or `v^(2) = (0.3)(10)((CB)/(BO))=(3xxR)/(sqrt(l^(2)-R^(2)))`
`or v^(2) = (3xx3)/(sqrt((0.5)^(2)-(0.3)^(2)))=(3xx0.3)/(0.4)=9/4 " " or v = 3/2 = 1.5` m/s