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Block m is released from rest when sprin...

Block `m` is released from rest when spring is in its natural length `(` assume pulley is ideal and block does not strike on ground during it's motion in vertical plane `)`
than `:`

A

maximum elongation in spring is `4mg//k`

B

maximum elongation in spring is `2mg//k`

C

maximum speed of block is `2gsqrt((m)/(k))`

D

maximum speed of block is `gsqrt((m)/(k))`

Text Solution

Verified by Experts

The correct Answer is:
A, C
By energy conservation `(1)/(2)kx^(2)=mg(2x)`
`rArrx=(4mg)/(k)(` maximum elongation `)`
at equilibrium `kx=2mg`
`rArr x=(2mg)/(k)`
So `(K.E.)_(max)=mg(2x)-(1)/(2)kx^(2)`
`=2mg((2mg)/(k))-(1)/(2)k((2mg)/(k))^(2)`
`(1)/(2)mv_(max)^(2)=(2m^(2)g^(2))/(k)`
`rArr v_(max)=2gsqrt((m)/(k))`
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