A body of mass m is attached to the lower end of a spring whose upper end is fixed. The spring has negligible mass when the mass m is slightly pulled down and released, it oscillates with a time period of 3s. When the mass m is increased by 1 kg, the time period of oscillations becomes 5s. The value of m in kg is...........

A body of mass m is attached to the lower end of a spring whose upper

1.	A body of mass m is attached to the lower end of a spring whose upper end is fixed. The spring has negligible mass when the mass m is slightly pulled down and released, it oscillates with a time period of 3s. When the mass m is increased by 1 kg, the time period of oscillations becomes 5s. The value of m in kg is...........
Answer» `(16)/(9)` `(9)/(16)` `(3)/(4)` `(4)/(3)` Solution :Period of oscillation of SPRING `T= 2pi sqrt((m)/(K))` `therefore 3= 2pi sqrt((m)/(k))"""…….."(1)` Periodic time when 1 kg is ADDED to m and `5= 2pi sqrt((m+1)/(k))"""…….."(2)` Taking ratio of eqn. (2) and (1) `(5)/(3) = sqrt((m+1)/(m))` `therefore (25)/(9)= (m+1)/(m)""` [squaring] `therefore 25M = 9m+9` `therefore 16m = 9` `therefore m= (9)/(16)`.