A block of mass m is suspended in equilibrium by a light string and a light spring attached to a horizontal ceiling. The string makes an angle of 30^ with the ceiling, and the spring makes an angle of 60^ with the ceiling. If the string is suddenly cut, the magnitude of the initial acceleration of the block immediately after the cut is :

Step-by-step solution

Let the tension in the string be T and the spring force be F_s . In the initial equilibrium state, the net force on the block is zero: T + F _s + m g = 0 The string makes an angle of 30^ with the horizontal, and the spring makes an angle of 60^ with the horizontal. The angle between the string and the spring is 180^ - (30^ + 60^ ) = 90^ . Resolving forces along the direction of the string, the component of the spring force is zero. The component of gravity along the string is mg (90^ - 30^ ) = mg (60^ ) . Thus, T =