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Two plates each of the mass m are connec...

Two plates each of the mass m are connected by a massless spring as shown
A weight W is put on the upper plate which compresses the spring further. When W is removed, the entire assembly jumps up. The minimum weight W needed for the assembly to jump up when the weight is removed is just more than -

A

mg

B

2mg

C

3mg

D

4mg

Text Solution

Verified by Experts

The correct Answer is:
B
For lower block + ve lift `k x ge mg implies x ge (mg)/k`
W / E theorem `-mg(h+x)+(1/2kh^2-1/2kx^2)=0-0`
`implies-mgh-(m^2g^2)/(k)+1/2kh^2-1/2(m^2g^2)/k=0`
`implies (kh^2)/(2) -mgh -(3m^2g^2)/(2k)`
`h= (mgpmsqrt(m^2g^2+3m^2g^2))/k = (mgpm2mg)/k = (3mg)/k, (-mg)/k`
`W +mg = khimplies W +mg = 3mg implies W = 2mg`
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