Question

A block of mass $5\text{kg}$ tied at the end of a string is whirled round in a vertical circle of radius $1\text{m}$. The critical speed of the block at the top of its swing below which the string would slacken before the block reaches the top is
Take $(\text{g}=10{\text{m/s}}^2)$

• A. $10\text{m/s}$
• B. $100\text{m/s}$
• C. $0.1\text{m/s}$
• D. $\sqrt{10}\text{m/s}$

Answer 1

The correct option is D $\sqrt{10}\text{m/s}$

At highest point,
Tension, $T$ in the string $=0$

Writing the force equation at the top point we get,
$mg+T=\frac{m{v}_c^2}{l}$, at the top most point $T=0$
$mg=\frac{{mv}_c^2}{l}$

$v_c^2=lg$

$v_c=\sqrt{lg}=\sqrt{1\times \text{g}}=\sqrt{10}\text{m/s}$

Hence option D is the correct answer