Question

A balanced lever has two weights on it, the first with mass `3 kg` and the second with mass `24 kg`. If the first weight is `9 m` from the fulcrum, how far is the second weight from the fulcrum?

Answer 1

`r=1.125m`

Explanation:

Let `m_1=3kg` `m_2`=24kg
Let `W_1` and `W_2` be the weights of `m_1` and `m_2` respectively.
`implies W_1=m_1*g=3*9.8=29.4N`
`implies W_2=m_2*g=24*9.8=235.2N`

Since the lever is balanced so both the torques produced by `W_1` and `W_2` should be equal.

Let the mass `m_2` be at a distance from `r` from the fulcrum.

Let `tau_1` and `tau_2` be the torques produced by `W_1` and `W_2` respectively.
`tau_1=tau_2`
`implies W_1*9=W_2*r`
`implies 29.4*9=235.2*r`
`implies r=(29.4*9)/235.2=1.125m`
`implies r=1.125m`
Hence the second weight is at a distance of 1.125m from the fulcrum.