Question

A stone weighing $1\text{kg}$ is whirled in a vertical circle at the end of a rope of length $0.5\text{m}$. Stone completes the vertical circle with minimum possible speed. The velocity of the stone midway, when the string is horizontal is (Take $g=10{\text{m/s}}^2)$

• A. $\sqrt{20}\text{m/s}$
• B. $5\text{m/s}$
• C. $\sqrt{15}\text{m/s}$
• D. $3\text{m/s}$

Answer 1

The correct option is C $\sqrt{15}\text{m/s}$


Since, the stone is just completing the vertical circle.
$V_A=\sqrt{gR}$
Applying law of conservation of energy at $A$ and $B$
$U_A+K{E}_A=U_B+K{E}_B$
$mg\left(2R\right)+\frac{1}{2}m(\sqrt{gR}{)}^2=mg(R)+\frac{1}{2}m{v}_B^2$
$⟹mgR+\frac{1}{2}m\left(gR\right)=\frac{1}{2}m{v}_B^2$
$⟹v_B=\sqrt{3gR}$
$⟹v_B=\sqrt{15}\text{m/s}$
($\because R=0.5\text{m}$)