# 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

##### 1 Answer

May 30, 2018

#### 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

#"R.E = U"#

#1/2"Iω"^2 = "mg"("L")/2#

#1/cancel"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

#"v = L ω"#

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

#color(white)(v) = sqrt("3gL")#

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

#color(white)(v) = "5.4 m/s"#