In the illustrated arrangement, the ends P and Q of an inextensible string travel downwards with a uniform speed u . The pulleys A and B are fixed. The mass M moves upwards with a speed equal to

Step-by-step solution

Let the vertical distance of mass M from the horizontal line joining the pulleys be y and the horizontal distance between the vertical line passing through M and either pulley be x . The length of the string segment between the pulley and the mass M is l , given by: l^2 = x^2 + y^2 Differentiating with respect to time t : 2l dl dt = 2x dx dt + 2y dy dt Since the pulleys are fixed, x is constant, so dx dt = 0 . l dl dt = y dy dt The ends P and Q are pulled downwards with speed u , meaning the length l decreases at t