(B) Let the mass of the lighter stone be $m_1 = m$ and its radius be $r_1 = r$. Let its tangential speed be $v_1$.Let the mass of the heavier stone be

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(B) Let the mass of the lighter stone be $m_1 = m$ and its radius be $r_1 = r$. Let its tangential speed be $v_1$.Let the mass of the heavier stone be $m_2 = 3m$ and its radius be $r_2 = r/3$. Let its tangential speed be $v_2$.The centripetal force is given by $F = \frac{mv^2}{r}$.Given that the centripetal forces are equal: $F_1 = F_2$.$\frac{m_1 v_1^2}{r_1} = \frac{m_2 v_2^2}{r_2}$Substituting the values: $\frac{m v_1^2}{r} = \frac{3m v_2^2}{(r/3)}$$\frac{m v_1^2}{r} = \frac{9m v_2^2}{r}$$v_1^2 = 9 v_2^2$$v_1 = 3 v_2$Since $v_1 = n v_2$,we have $n = 3$.

Class 11 Physics 2 Motion in a Plane Dynamics of circular Motion (Centrifugal force) and Pendulum and Motion on Curved path

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Two stones of masses $m$ and $3m$ are whirled in horizontal circles,the heavier one in a radius of $(r/3)$ and the lighter one in a radius of $r$. The tangential speed of the lighter stone is $n$ times that of the heavier stone when they experience the same centripetal force. The value of $n$ is:

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

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2 Motion in a Plane

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Dynamics of circular Motion (Centrifugal force) and Pendulum and Motion on Curved path

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Two stones of masses $m$ and $3m$ are whirled in horizontal circles,the heavier one in a radius of $(r/3)$ and the lighter one in a radius of $r$. The tangential speed of the lighter stone is $n$ times that of the heavier stone when they experience the same centripetal force. The value of $n$ is:

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