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Rich temporal information and variations in viewpoints make video data an attractive choice for learning image representations using unsupervised contrastive learning (UCL) techniques. State-of-the-art (SOTA) contrastive learning techniques consider frames within a video as positives in the embedding space, whereas the frames from other videos are considered negatives. We observe that unlike multiple views of an object in natural scene videos, an Ultrasound (US) video captures different 2D slices of an organ. Hence, there is almost no similarity between the temporally distant frames of even the same US video. In this paper we propose to instead utilize such frames as hard negatives. We advocate mining both intra-video and cross-video negatives in a hardness-sensitive negative mining curriculum in a UCL framework to learn rich image representations. We deploy our framework to learn the representations of Gallbladder (GB) malignancy from US videos. We also construct the first large-scale US video dataset containing 64 videos and 15,800 frames for learning GB representations. We show that the standard ResNet50 backbone trained with our framework improves the accuracy of models pretrained with SOTA UCL techniques as well as supervised pretrained models on ImageNet for the GB malignancy detection task by 2-6%. We further validate the generalizability of our method on a publicly available lung US image dataset of COVID-19 pathologies and show an improvement of 1.5% compared to SOTA. Source code, dataset, and models are available at https://gbc-iitd.github.io/usucl.