Question

A stationary marble with mass M rolls down a hill with height H. Determine the velocity of the marble at the bottom of the ramp.

Start your initial statement with E0 = Ef

Answer 1

Answer:
`v=\sqrt{(10)/(7)gH}`

Step-by-step explanation:

Given

Marble rolls down the hill

Considering it to be a solid sphere of radius R

Conserving the total Energy as it is constant

`E_0=E_f\quad [\text{as initial energy=Final energy}]`

`MgH=(1)/(2)Mv^2+(1)/(2)I\omega ^2`

where I=moment of inertia of marble

`((2)/(5)MR^2)`

Considering pure rolling

so
`v=\omega * R`

`MgH=(1)/(2)Mv^2+(1)/(2)* (2)/(5)MR^2* ((v)/(R))^2`

`gH=(7)/(10)v^2`

`v=\sqrt{(10)/(7)gH}`