A) \[\frac{mg}{k}\]
B) \[2d\]
C) \[\frac{mg}{3k}\]
D) \[4d\]
Correct Answer: B
Solution :
Case 1: If block is released slowly, Given, spring constant = k When mass m is suspended from spring, then d extension is developed in spring. From law of conservation of energy \[mgh=\frac{1}{2}k{{d}^{2}}+mg(h-d)\] \[mgh=\frac{1}{2}k{{d}^{2}}+mgh-mgd\] \[mgd=\frac{1}{2}k{{d}^{2}}\] \[\Rightarrow \] \[d=\frac{2\,mg}{k}\] ?(i) \[\Rightarrow \] \[k=\frac{2mg}{d}\] Case 2: Again if block is released suddenly, further, then again, from law of conservation of energy \[mgh=\frac{1}{2}k{{(d+y)}^{2}}+mg(h-d-y)\] \[mg(d+y)=\frac{1}{2}k{{(d+y)}^{2}}\] \[mg(d+y)=\frac{1}{2}\frac{2mg}{d}({{d}^{2}}+{{y}^{2}}+2dy)\] \[{{d}^{2}}+dy={{d}^{2}}+{{y}^{2}}+2dy\] \[\Rightarrow \] \[y(y+d)=0\] \[y=-d\] \[\therefore \] Total displacement = (2d)You need to login to perform this action.
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