Question

The passengers in a boat are not allowed to stand because:
A) This will raise the centre of gravity and the boat will rock
B) This will lower the centre of gravity and the boat will rock
C) The effective weight of the system increases
D) Due to surface tension effects

Answer 1

A boat may topple when it is subjected to undue torque from waves or the wind which tries to rotate the boat such that it becomes upside down. The effect of this torque will depend upon the radial distance of the centre of gravity of the boat and passenger system from the axis of rotation (longitudinal axis of the boat).

Complete step by step answer:
A boat usually topples, that is, rotates upside down about an axis that passes through the centre and connects the longitudinal ends of the boat, that is, the front to the back. This can happen when the system of the boat along with its passengers is subjected to a great torque either from the waves on the water or wind flowing.
The effect of the torque depends upon the radial distance of the centre of gravity of the system of boat and passengers from the longitudinal axis. Greater the radial distance, greater will be the torque on the boat and greater will be the chances of it toppling.
If the passengers in the boat stand up, in effect, they raise the centre of gravity of the system and hence, increase the radial distance of the centre of gravity from the axis of rotation. This leads to an increase in the chances of the boat rocking as the torque offered by the wind, waves and other forces, also increases.
This increased rocking can be potentially dangerous for the boat and all the passengers aboard.
Therefore, the passengers in a boat are not allowed to stand up.
Therefore, the correct option is A) This will raise the centre of gravity and the boat will rock.

Note:
A similar principle is applied in race cars which have a very low centre of gravity. This enables that when they take corners at high speed, they are not easily rocked and toppled by the lateral centrifugal forces that act on the car.
Students must not think that standing up will increase the effective weight of the system. There will be no effect on the effective weight of the system since weight depends upon the mass of the system and the acceleration due to gravity, both of which remain the same regardless of whether the passengers stand up or sit down.