Question

A bob is whirled in a horizontal circle by means of a string at an initial speed of 10 rpm. If the tension in the string is quadrupled while keeping the radius constant, the new speed is:

• A. 20 rpm
• B. 40 rpm
• C. 5 rpm
• D. 10 rpm

Answer 1

The Correct Option is A

Tension in String During Circular Motion 

1. Centripetal force provided by tension

For an object in uniform circular motion, tension $T$ provides the centripetal force:

$$ T = \frac{mv^2}{r} $$

Where $m$ = mass, $v$ = speed, $r$ = radius

2. Proportionality relation

With mass $m$ and radius $r$ constant:

$$ T \propto v^2 $$

If tension increases 4 times:

$$ T_2 = 4T_1 \quad \Rightarrow \quad v_2^2 = 4v_1^2 $$

3. Given initial speed

$$ v_1 = 10 \, \text{rpm} $$

Then:

$$ v_2 = \sqrt{4} \times v_1 = 2 \times 10 \, \text{rpm} $$

$$ v_2 = 20 \, \text{rpm} $$

New speed $v_2 = 20 \, \text{rpm}$

Doubling the speed quadruples the tension, since $T \propto v^2$.