# A meter scale is held vertically with one of the ends on the floor without slipping.the velocity of the upper end of the scale when it hits the floor is?? 9.8m/s 8.9 45 5.4

May 30, 2018

$\text{5.4 m/s}$

#### Explanation:

Initial potential energy of centre of mass of scale is

"U" = "mg"("L")/2

Scale falls without slipping. Therefore the total potential energy is converted into rotational energy

$\text{R.E = U}$

1/2"Iω"^2 = "mg"("L")/2

$\frac{1}{\cancel{\text{2"(cancel"m""L"^2)/3"ω"^2 = cancel"m""g"("L")/cancel"2}}}$

ω = sqrt("3g"/"L")

Velocity of upper end of scale when it hits the ground is

$\text{v = L ω}$

color(white)(v) = "L" sqrt("3g"/"L")

$\textcolor{w h i t e}{v} = \sqrt{\text{3gL}}$

color(white)(v) = sqrt(3 × "9.8 m/s"^2 × "1 m")

$\textcolor{w h i t e}{v} = \text{5.4 m/s}$