If the radius of the circular path is increased while the speed of the block remains constant, the graph of the relationship between the radius and the tension in the string would look like an upward sloping line.
The tension in the string is responsible for providing the centripetal force that keeps the block moving in a circular path. The centripetal force is given by the equation:
F_c = (m * v^2) / r
Where: F_c is the centripetal force, m is the mass of the block, v is the velocity of the block, and r is the radius of the circular path.
Since the speed remains constant, the equation can be rearranged as:
F_c = (m * constant) / r
As the radius increases, the tension in the string decreases because the force required to maintain the circular motion decreases. This is because the centripetal force is inversely proportional to the radius.
So, on the graph, the tension (T) would be plotted on the y-axis, and the radius (r) would be plotted on the x-axis. The graph would show a decreasing trend as the radius increases. It would start with a higher tension value at smaller radii and gradually decrease as the radius increases. The graph would be a downward sloping line.