A bullet of mass m moving with a velocity v collides head on with a block of mass m which is placed on a car of mass 4m. Bullet gets embedded in the block. The block is connected with car by massless spring of constant k. Find the maximum compression x of the spring. Neglect friction everywhere.

Dear Abdul , Always apply the two principles given below , trying with the force approach maybe complex,

Momentum conservation:

momemtum of bullet = momentum of (bullet + mass m +car)

mv =(m+m+4m) .v2

therefore , v2 = v/6

energy conservation:

 k.e of energy of bullet  = k.e of ( car +mass+ bullet ) + p.e of spring

1/2 * m* v²  = 1/2*(m+m+4m)*(v/6)²  + 1/2 *k *x²

5mv²/6 =  kx²

x = (5mv²/6k)^1/2

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Sir,

Thanks alot for spending your precious time. My approach is exactly same as yours. But unforunately the answer is not correct.

the correct answer is x=v(m/3k)^1/2