Question

7. A block of mass M is held at rest on a horizontal table. A heavy chain is attached to the block with part of the chain hanging over the table. The block and the chain can slide without friction. block table chain The block is released. Which one of the following graphs best represents the variation with time t of the speed v of the block as it moves on the table? 1 B. C. OL 0 0

Answer 1

Let mass of change be m & length be L mass m� of hanging part is m� = m/L y so force on system is F = m� g = m/L y g so acceleration of system is a = F/(M + m) = mg/L (M + m) y = K Y {K = mg/(M + m) L} V dv/dy = ky implies integral^u_0 v dv = k integral^y_0 y dy V^2 /2 = k y^2 /2 implies V = squareroot k y a = dv/dt implies a = squareroot K dy/dt implies a = squareroot k v dv/dt = squareroot k v implies integral^u_v_0 dv/v = squareroot k integral^t_0 dt v/v_0 = squareroot k t implies v = v_0 e^squareroot k t