Question

A mass attached to one end of a string crosses top-most point on a vertical circle with critical speed. Its centripetal acceleration when string becomes horizontal will be (g = gravitational acceleration)

• A. $g$
• B. $3\,g$
• C. $4\,g$
• D. $6\,g$

Answer 1

Answer: (B)

$3\,g$

Answer 2

We know that,
velocity of particle at top-most point on vertical circle,
$\left(v_{\text {top }}\right)=\sqrt{3 r g} \,\,\,\, \,\, ...(i)$
But centripetal acceleration $\left(a_{c}\right)=\frac{v^{2}}{r}$
$\therefore \,\,\,\,\,\, a_{c} =\frac{(\sqrt{3 r g})^{2}}{r} \,\,\,\,\,\,\,\,$ [from E (i)]
$a_{c} =\frac{3 r g}{r}$
$a_{c} =3\, g$