Question

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

• A. $7r.p.m.$
• B. $14r.p.m.$
• C. $10r.p.m.$
• D. $20r.p.m.$

Answer 1

Answer: (A)

$7r.p.m.$

Given : $m=2kg$

Initial speed of rotation $f_1=5$ $r.p.m$

Let the radius of the circle be $r$

$\therefore$ Tension in the string $T_1=mr{w}_1^2$ where $w_1=2\pi f_1$

$⟹$ $T_2=4{\pi }^{2}mr{f}_1^2$ ....................(1)

Now the tension in the string is doubled i.e $T_2=2T_1$

$\therefore$ $T_2=4{\pi }^{2}mr{f}_2^2$

OR $2T_1=4{\pi }^{2}mr{f}_2^2$ ..........(2)

Dividing (2) by (1), $2=\frac{f_2^2}{5^2}$ $⟹f_2\approx 7$ $r.p.m$