You are holding a shopping basket at the grocery store with two 0.60 kg cartons of cereal at one end of the basket. The basket is 0.77 m long. Where should you place a half gallon of milk (1.8 kg) so that the center of mass (COM) of your groceries is at the center of the basket

The gallon of milk is placed at a distance of 0.641 meters.

Explanation:

We have,

Mass of two 0.6 kg cartons of cereal is 1.2 kg

Length of the basket, l = 0.77 m

Center of the basket is 0.385 m

Mass of the half gallon of milk is 1.8 kg

Total weight in the basket is 1.2 + 1.8 = 3 kg

We need to find the position of the gallon of milk so that the center of mass (COM) of your groceries is at the center of the basket.

So,

(3 * 0.385) = (1.2 * 0) + (1.8 * x)

1.155 = 1.8 x

x = 0.641 meters

So, the gallon of milk is placed at a distance of 0.641 meters.