Question

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

Answer 1

`"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

`"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"`