Question

A particle is moving in a circular path in the vertical plane. It is attached at one end of a string of length $l$ whose other end is fixed. The velocity at lowest point is $u$. The tension in the string is $\overrightarrow{T}$ and acceleration of the particle is $\overrightarrow{a}$ at any position. Then $\overrightarrow{T}.\overrightarrow{a}$ is zero at highest point if

• A. $u>\sqrt{5gl}$
• B. $u=\sqrt{5gl}$
• C. Both (a) and (b) correct
• D. Both (a) and (b) are wrong

Answer 1

Answer: (B)

$u=\sqrt{5gl}$

Tension is $0$in case of $B$.

If $u$is more than this, then Tension is never zero.

if $u$is less than this, then the particle would never be able to complete the circular loop.

$m{v}^2/r=mg\frac{m{u}^2}{2}=2\times mgR+\frac{m{v}^2}{2}\Rightarrow u=\sqrt{5Rg}$