Two stones of masses m and 2m are whirled in horizontal circles, the heavier one in a radius r2, and the lighter one in radius r. The tangential speed of the lighter stone is n times that of the heavier stone when they experience the same centripetal forces. The value of n is:

Centripetal force is same on both as given.
Let v1 be the tangential speed of the lighter stone (mass m) and v2 be the tangential speed of the heavier stone (mass 2m).
Let r be the radius of the circle for the lighter stone and r2 be the radius of the circle for the heavier stone.
The centripetal force for the lighter stone is given by:
F1 = mv1²/r
The centripetal force for the heavier stone is given by:
F2 = 2mv2²/r2
Given that F1 = F2, we have:
mv1²/r = 2mv2²/r2
Since v1 = nv2 (the tangential speed of the lighter stone is n times that of the heavier stone), we can substitute this into the equation:
m(nv2)²/r = 2mv2²/r2
n²mv2²/r = 2mv2²/r2
We can cancel out mv2² from both sides:
n²/r = 2/r2
n² = 2r/r2
n = √(2r/r2)
Without knowing the values of r and r2, we cannot find a numerical value for n. However, if we assume a scenario where r = r2, then:
n = √(2r/r) = √2 ≈ 1.414
None of the given options match this result. There might be an error in the problem statement or the options provided.