Question

A balanced lever has two weights on it, the first with mass `9 kg` and the second with mass `32 kg`. If the first weight is `6 m` from the fulcrum, how far is the second weight from the fulcrum?

Answer 1

`27/16` m.

Explanation:

For a balanced lever the torque on the two ends must be equal.

Torque can be defined as `"mass" xx "distance from fulcrum"`

So
`color(white)("XXX")m_1xxd_1 = m_2 xx d_2`

or for the given data:
`color(white)("XXX")9 " kg"xx6" m" = 32" kg" xx d_2 " m"`

`color(white)("XXX")d_2=(9xx6)/32 " m" = 27/16" m"`

Answer 2

Second weight is `54/32=1.6875` `m` far from fulcrum.

Explanation:

Let the the second weight be `x` m far from the fulcrum.

As the lever is balanced, moment (`M=F*d`, where `F` is force applied and `d` is its distance from fulcrum) of the two weights should be equal.

Moment of first weight is `9*6=54` and as it balances second weight of `32` kg, the latter's distance should be

`54/32=1.6875` `m`.