KVPY SB SX Exam 2011 Question Paper

Question : 22 of 120

Marks: +1, -0

Two plates each of 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

Validate

Solution:

For lower block +ve lift, kx ≥ mg

⇒x ≥ \mg/\k

W/E theorem

-mg(h+x)

+(1/2kh^2-1/2kx^2)=0-0

⇒-mgh-{m^2g^2}/k+

1/2kh^2-1/2{m^2g^2}/k=0

{kh^2}/2-mgh-{3m^2g^2}/{2k}=0

h={mg±√{m^2g^2+3m^2g^2}}/k

={mg±2mg}/k

={3mg}/k,-{mg}/k

∴h={3mg}/k

W + mg = kh
W + mg = 3mg
W = 2mg

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