A uniform solid disc of mass M and radius R is held horizontally and suspended by two identical vertical inextensible strings attached to opposite ends of one of its diameters. If one of the strings is suddenly cut, the tension in the remaining string immediately after the cut is ( g is acceleration due to gravity)

Step-by-step solution

Let the strings be attached at points A and B, which are the ends of a diameter. When the string at B is cut, the disc will instantaneously rotate about a horizontal axis passing through A and perpendicular to the diameter AB (i.e., the tangent to the disc at A). Moment of inertia of the disc about its diameter is I_ d = MR^2 4 . By parallel axis theorem, moment of inertia about the tangent at A is: I_A = I_ d + MR^2 = MR^2 4 + MR^2 = 5MR^2 4 Torque about A is provided by the weight of the disc acting at its center