Work, Power and EnergyHard
Question
In the given figure a ball of mass m is connected to an elastic spring of force constant K = mg/L through an inextensible string as shown. Now the ball is released from rest.
Options
A.The maximum velocity of mass m during fall is 
B.The maximum velocity of mass m during fall is 
C.The maximum potential energy stored in the spring during the fall is mgL [2 + √3]
D.The maximum potential energy stored in the spring during the fall is mgL [3 + √2]
Solution
Using energy conservation between initial moment and equilibrium moment when T = mg.
× L2 + 
mv2 = mg × 2L
V =
If ball falls a maximum distance of L + x.
mg(L + x) =
x2
x = L(1 + √3)
∴ PEmax = mgL(2 + √3)
× L2 + mv2 = mg × 2LV =
If ball falls a maximum distance of L + x.
mg(L + x) =
x2x = L(1 + √3)
∴ PEmax = mgL(2 + √3)
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