ANS:A - two

The expected efficiency of a single riveted lap joint is given as 50%, which means that half of the strength of the plate is utilized in the joint. When the thickness of the plate is increased four times, it implies that there will be more material to support the load, potentially increasing the overall strength of the joint. To maintain the same efficiency of 50%, the rivet diameter will need to be increased to compensate for the increased thickness of the plate. The cross-sectional area of the rivet should be proportional to the cross-sectional area of the plate to maintain the same efficiency. Since the thickness of the plate is increased four times, the diameter of the rivet needs to be increased to √4 = 2 times the original diameter to maintain the same cross-sectional area. Therefore, the rivet diameter will have to be increased two times.