Question

The velocity of a particle executing SHM is 50% of its maximum value at an instant of time. At that moment, acceleration is _____% of its maximum value.

• A. 50
• B. 86.6
• C. 75
• D. 64.6

Answer 1

The correct option is B 86.6

$Vmax=A\omega$
$V=\omega \sqrt{A^2-x^2}$
$V=\frac{Vmax}{2}$
$\frac{A\omega }{2}=\omega \sqrt{A^2-x^2}$
$\Rightarrow x=\frac{\sqrt{3}}{2}A$
$a_{max}={\omega }^{2}A$
$a={\omega }^{2}x$
$\frac{a}{a_{max}}\times 100=$ % of $a_{max}$
% of $a_{max}$$=\frac{\frac{\sqrt{3}}{2}\times A{\omega }^2}{A{\omega }^2}\times 100$$=86.6$