Three blocks of masses (700 ~g , 500 ~g ) and (400 ~g ) suspended at the end of a spring as shown in the figure, are in equilibrium. When the (700 ~g ) block is removed, the system has a period of oscillations of (3 ~s ). If both (700 ~g ) and (500 ~g ) blocks are removed, the period of oscillation becomes

Step-by-step solution

The given situation is shown in the following figure When the block of (700 ~g ) is removed, then period of oscillation is given as ( aligned T^ & =2 m k & =2 (700+500+400-700) 10⁻³ k aligned ) [where, (k= ) spring constant] (T^ =2 0.9 k ) But ( T^ =3 ~s ) ( 3=2 0.9 k 9=4 ^2 0.9 k ) ( k=0.4 ^2 ) ...(i) When both blocks of (700 ~g ) and (500 ~g ) are removed, then period of oscillation is given as ( array rlr T^ & =2 (700+500+400-700-500) 10⁻³ k & =2 0.4 0.4 ^2 & = 2 =2 ~s array )