Question

A mass of $2kg$ is whirled in a horizontal circle by means of a string at an initial speed of $5rpm$. Keeping the radius constant, the tension in the string is doubled. The new speed is nearly

• A. $14rpm$
• B. $10rpm$
• C. $7rpm$
• D. $20rpm$

Answer 1

Answer: (C)

$\text{Step 1: Drawing Free body diagram}$ $\text{[Ref. Fig.]}$

Let $r$ be the radius of circle.

$\text{Step 2: Apply Newton's second law}$

Solving in ground frame:

Applying Newton's second Law on mass (m) along centripetal direction (considering direction towards centre as Positive)

$\sum F_c=m{a}_c$

$T=mr{w}^2$

$\text{From initial condition FBD}$

$T=mr{w}^2$ $....\left(1\right)$

$\text{From Final condition FBD}$

$2T=mr{w}_2^2$

$w_2^2=\frac{2T}{mr}$ $....\left(2\right)$

$\text{Step 3: Equation solving}$

Substituting value of $T$ in equation $\left(2\right)$

$w_2^2=\frac{2mr{w}^2}{mr}$

$\Rightarrow$ $w_2=\sqrt{2}w$

$\Rightarrow w_2=\sqrt{2}\times 5rpm$ $\approx 7rpm$

Hence, option $C$ is correct answer.