Get Products by Category ids ? with short code !

how can i get a list of products with the id of their category?!
in the code below $pid is what the user type in shortcode, ‘object_id’ is the id of the every product in wp_posts table.

<?php
    $products = $wpdb->get_results("SELECT object_id FROM {$wpdb->term_relationships}
                                      WHERE term_taxonomy_id = " . $pid);
    if(!empty($products))
    {
        foreach($products as $product)
        {
            //the code
        }
    }
?>