An answer to Rhodesia is an answer to black America," announced the powerful and angry voice of Randall Robinson from the front of the ballroom.

That challenge to President Carter, on his pending decision whether to recognize the new Rhodesian government, changed last night's TransAfrica dinner from a social event into "a mobilization meeting."

"The Senate recently voted to lift sanction against Rhodesia," said Robinson, TransAfrica's executive director, "the president has nothing . . . the secretary of state said it presented curiously a new reality. We have been struggling against injustice and we know freedom when we see it."

As a thousand people seated in the Shoreham Americana Hotel cheered, Robinson warned the administration that approval of the new Rhodesian government would cause a backlash in America's black community. "If he does (recognize the new government), he is not going back to the White House," Robinson said. The dinner's main speaker, U.S. Ambassador to the United Nations Andrew Young, applauded vigorously. But later, Young leaned back in his chair when the withdrawal of black support for Carter in next year's election was mentioned. Carter won an overwhelming majority of the black vote in the '76 election.

Reinforcing the challenge to the Carter administration, Richard Hatcher, the mayor of Gary, Ind., and the chairman of TransAfrica's board, said, "Support for either one of these regimes (Rhodesia or South Africa) is a blow for black America.We will not tolerate . . . one more hostile act against black people."

When he spoke, Young said he was not discouraged by the recent Senate vote to lift sanctions against Rhodesia, and he indicated that President Carter would make a decision in line with Young's own feelings and that of his black constituency.

"The president understands this just as well as everyone else. His problem is how to get support," said Young, describing the bureaucracy of the State Department and the roadblocks in Congress. "People who are pushing these resolutions don't know about Africa. They don't give a damn about Africa. They know the way to split the Democratic party is to raise the African issue."

At its first fund-raising dinner last year, only 500 people celebrated the beginning of TransAfrica, the only lobbying group of black Americans for African and Caribbean issues. Last night the number had doubled.

"Already TransAfrica has had the most profound effects because in the past there was always an excuse in the congressional committees that black Americans weren't interested. That can't be said any more," said Rep. Cardiss Collins (D.-Ill.), the chairman of the Congressional Black Caucus and a member of the House Foreign Affairs Committee.

Though TransAfrica has lobbied vigorously on the whole spectrum of political and social problems in southern Africa, it has drawn criticism regarding its priorities and makeup. Vivian Anderson, an officer with AID, observed last night, "I'm afraid what's happening is than TransAfrica made a big splash in certain cities around the country but then didn't follow up. There's a great interest and lots of workers out there. The organization has to move beyond Washington."

Last night's audience had broadened beyond its natural constituency of foreign policy shapers to include lawyers, physicians and educators. Some of the African-interest groups had privately expressed annoyance with Ambassador Young, who last week voted to allow South Africa to participate in the U.N. General Assembly debate on Naimibia. The move was defeated with the U.S. and 15 other countries standing against the African bloc.

"We disapprove of Young's vote. We think South Africa should be expelled totally and isolated," said Randall Robinson. "He has to be viewed as an instrument of this administration," said Mel McCaw, Washington director of the African-American Institute. Yet none of this criticism surfaced at the dinner.

The diplomats were predictably diplomatic. "I don't think the African or the Caribbean countries think that [Young's vote] reflects on him personally," said Alfred Rattray, the ambassador from Jamaica. "I imagine he is following the instructions of his government." CAPTION: Picture 1, From left, Andrew Young, Cardiss Collins, Richard Hatcher and Randall Robinson, by Tom Allen - The Washington Post; Picture 2, John Ray, left, and Carl Rowan, by Tom Allen - The Washington Post