A uniform beam of length L and mass m is supported as shown. The cable at B suddenly breaks. Which option correctly gives both (i) the acceleration of end B and (ii) the vertical reaction at the pin immediately after the break?

Question

G1 Physics · Accepted Answer

After the cable breaks, take moments about the pin. With the dimensions shown, torque about A=Iₐα gives the angular acceleration of the beam; the end acceleration is acceleration of B=αL. Substituting the given geometry yields acceleration of B=9g/7 downward. Then use vertical force balance=ma of CM to obtain the pin reaction reaction at A=4mg/7 upward. Therefore option B.