A uniform, thin cylindrical shell and solid cylinder roll horizontally without slipping. The speed of the cylindrical shell is v . The solid cylinder and the hollow cylinder encounter an incline that they climb without slipping. If the maximum height they reach is the same, find the initial speed v' of the solid cylinder.

Question

A uniform, thin cylindrical shell and solid cylinder roll horizontally without slipping. The speed of the cylindrical shell is v . The solid cylinder and the hollow cylinder encounter an incline that they climb without slipping. If the maximum height they reach is the same, find the initial speed v' of the solid cylinder. (A) √(4/3)v (B) √(3/4)v (C) √(3/5)v (D) √(5/3)v

Tardigrade Admin · Accepted Answer

KE=(1/2)m v2+(1/2)Iω 2 (3/4)m v12=m v22 (v1/v2)=√(4/3)

$\frac{4}{3} v$

$\frac{3}{4} v$

$\frac{3}{5} v$

$\frac{5}{3} v$

$K E = \frac{1}{2} m v^{2} + \frac{1}{2} I ω^{2}$
$\frac{3}{4} m v_{1}^{2} = m v_{2}^{2}$
$\frac{v _{1}}{v _{2}} = \frac{4}{3}$

34​​v

43​​v

53​​v

35​​v

KE=21​mv2+21​Iω2 43​mv12​=mv22​ v2​v1​​=34​​

$\frac{4}{3} v$

$\frac{3}{4} v$

$\frac{3}{5} v$

$\frac{5}{3} v$

$K E = \frac{1}{2} m v^{2} + \frac{1}{2} I ω^{2}$
$\frac{3}{4} m v_{1}^{2} = m v_{2}^{2}$
$\frac{v _{1}}{v _{2}} = \frac{4}{3}$