Falls Church, the nation's second wealthiest city, is finding that most of its residents could not afford to live there if they had to buy their houses at today's prices and interest rates.

Based on the fact that average apartment rentals in Falls Church are the highest in Northern Virginia and that the cost of owning a home is escalating, a city planning study has concluded the majority of area residents are precluded from moving into Virginia's smallest city and high prices "are threatening to force existing households out."

The "housing affordability crisis" in the city, shared to a lesser extent by most area jurisdictions, is cited by the study as grounds for changing the city's master plan to permit more apartment buildings and condominiums.

The City Planning Commission will hold two public hearings on the issue, July 18 and Aug. 15, both at 8 p.m. in City Hall.

The study found that family size in Falls Church decreased between 1970 and 1980, while the number of households increased 51 percent in the city, changes caused in large part by the increase in the number of single-parent families and elderly residents.

While Falls Church has a relatively large number of rental units--just more than 52 percent of housing units are rented--most of them are expensive. The average median rent in 1980 was more than $360 a month, higher than any other Northern Virginia jurisdiction.

City houses are not as expensive on an average as those in Alexandria and Arlington, but their average value in 1980 of $89,000 would make them unaffordable to 64 percent of area residents and 65 percent of present city residents. The only reason current residents can afford to live in Falls Church, the report concludes, is that 87 percent of them bought their homes before 1978, when interest rates were still less than 10 percent and house prices were much lower.