A pan with a set of weights is attached to a light spring. The period of vertical oscillation is 0.5 s . When some additional weights are put in pan, then the period of oscillations increases by 0.1 s . The extension caused by the additional weight is

Step-by-step solution

Given, T=0.5 ~s , We know that, T=2 m k 0.5=2 m k 1 4 = m k On squaring both sides, we get m k = 1 16 ^2 ...(i) aligned & T+0.1=2 m+m^ k & 0.5+0.1=2 m+m^ k & ( 0.6 2 )^2= m+m^ k = m k + m^ k & aligned ( 0.6 2 )^2= 1 16 ^2 + m^ k [using Eq. (i)] (0.6)^2 4 ^2 - 1 16 ^2 = m^ k m^ k = 1.44-1 16 ^2 m^ k = 0.44 16 ^2 ....(ii) aligned & m^ g & =k x & x & = m^ k g aligned = 0.44 16 ^2 10 [using Eq. (ii)] aligned & =0.0279 & =2.79 10⁻² ~m & =2.7 ~cm aligned