91Ó°ÊÓ

At equilibrium, the net torque is zero.For this problem, the clockwise torque due to the weight of the woman is equal to the torque due to the board's weight.

The mass of the woman is \(m = 60\;{\rm{kg}}\).

The length of the board is l.

The pivot point is at a distance \(\frac{l}{4}\) from the right end of the board.

Let M be the mass of the board.

You can consider the board as a single rod. So, the mass of the board is at the middle of the board, i.e., the distance of the board's mass is at \(\frac{l}{4}\) to the left of the pivot point.

Now, at equilibrium, the counter-clockwise torque is equal to the clockwise torque. Then,

\(\begin{aligned}{c}Mg \times \frac{l}{4} = mg \times \frac{l}{4}\\M = m\\ = 60\;{\rm{kg}}\end{aligned}\).

Hence, the mass of the board is 60 kg.

Hence, option (d) is correct.