When a body of mass 1.0 ~kg is suspended from a certain light spring hanging vertically, its length increases by 5 ~cm . By suspending 2.0 ~kg block to the spring and if the block is pulled through 10 ~cm and released, the maximum velocity in it in m / s is : (Acceleration due to gravity =10 ~m / s ^2 )

Step-by-step solution

m₁=1 ~kg , extension l₁=5 ~cm =5 10⁻² ~m m₁ g=k l₁k= force constant of the spring k= m₁ g l₁ = 1 10 5 10⁻² =200 ~N / m Time period of the block of mass 2 ~kg , T=2 m k =2 2 200 =2 1 10 = 5 ~s Maximum velocity, v_ =A where, A= amplitude =10 ~cm =10 10⁻² ~m v_ =A 2 T =10 10⁻² 2 / 5 =10⁻¹ 2 5=1 ~m / s