Question

Two stones of masses \( m \) and \( 3m \) are whirled in horizontal circles, the heavier one in radius \( \dfrac{r}{3} \) and lighter one in radius \( r \). The tangential speed of lighter stone is \( n \) times that of the heavier stone when both experience the same centripetal force. The value of \( n \) is

• A. 2
• B. 3
• C. 1
• D. 4

Hint:

When centripetal forces are equal, relate mass, radius, and speed carefully before solving.

Answer 1

The Correct Option is B

Step 1: Write the formula for centripetal force.
\[ F = \frac{mv^2}{r} \]
Step 2: Write force equations for both stones.
For lighter stone: \[ F = \frac{m v_1^2}{r} \] For heavier stone: \[ F = \frac{3m v_2^2}{r/3} \]
Step 3: Equate the forces.
\[ \frac{m v_1^2}{r} = \frac{3m v_2^2}{r/3} \]
Step 4: Simplify.
\[ \frac{v_1^2}{r} = \frac{9 v_2^2}{r} \Rightarrow v_1^2 = 9 v_2^2 \Rightarrow v_1 = 3 v_2 \]
Step 5: Conclusion.
The tangential speed of the lighter stone is 3 times that of the heavier stone.