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 [2024]

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Solution

Q.
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 [2024]

1 20 rpm

2 40 rpm

3 5 rpm

4 10 rpm

Ans.
(1)

Let $r$ be radius of circle.

Here, tension provides the required centripetal force,

$\sum F_{c} = m a_{c}$

So, from initial condition,

$T = m r ω^{2}$ ...(i)

and, from final condition,

$4 T = m r ω'^{2}$ ...(ii)

From eqn. (i) and (ii), we get

$\frac{T}{4 T} = \frac{m r ω^{2}}{m r ω'^{2}} \Rightarrow \frac{1}{4} = \frac{ω^{2}}{ω'^{2}} \Rightarrow ω'^{2} = 4 ω^{2}$

$ω' = 2 ω = 2 \times 10 = 20 rpm$

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