A balloon and a mass are attached to a rod that is pivoted at P. The balloon is filled with helium, a gas less dense than air, so that it applies an upward force on
the rod.

The rod is horizontal and stationary.
Which action causes the rod to rotate clockwise?

A Move both the balloon and mass 10 cm to the left.
B Move both the balloon and mass 10 cm to the right.
C Move both the balloon and mass to the 25 cm mark.
D Move the balloon to the 20 cm mark and the mass to the 30 cm mark.

The correct option is;

B Move both the balloon and mass 10 cm to the right

Explanation:

Given that the system is in equilibrium, we have;

Force of balloon = ↑

Force of mass = ↓

The direction of the balloon is having an upward motion which gives a clockwise moment or motion to the rod while the direction of the force of the mass weight is downwards, giving the rod an anticlockwise moment

for the rod to rotate clockwise, the moment of the balloon should be larger than that of the rod

At the present equilibrium we have;

× 30 =   × 20

Therefore;

= 1.5×

Moving both balloon and mass 10 cm to the right gives;

The moment of the balloon = × (30 - 10)  = × 20 = 20×,

The moment of the mass =   × (20 - 10) =   × 10

When we substitute   = 1.5× in the moment equation for the mass, we have;

The moment of the mass = × 10 = 1.5× ×10 = 15×

Therefore, the balloon now has a larger momentum than that of the mass and the rod will rotate clockwise.