Two stones of masses m and 2 m are whirled in horizontal circles, the heavier one in a radius and the lighter one in radius `r/2.` The tangential speed of lighter stone is n times that of the value of heavier stone when they experience same centripetal forces. The value of n is:

Options

A. 1
B. 2
C. 3
D. 4

Answer

B

Explanation

`(f_(c)) _("heavier")= (f_(c)) _("lighter")`
`therefore = (2mv _(1) ^(2))/( (r)/(2)) = ( mv _(2) ^(2))/( r )`
`therefore 4v _(1) ^(2) = v _(2) ^(2) `
`therefore 2v_(1) =v_(2)`
`therefore 2v_(1) = nv_(1) " "[because v _(2) = nv_(1) ]`
`therefore 2=n`
`therefore n =2`