In a two block system an initial velocity $v_{0}$ (w.r.t. ground) is given to block $A$ , which is placed on a stationary block $B$ as shown in the figure. Which of the following is true :

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the increase in momentum of $B$ is equal to the decrease in momentum of block $A$

the momentum of block $A$ is not conserved

the increase in kinetic energy of $B$ is less than decrease in $K E$ of $A$ .

the increase in kinetic energy of $B$ is equal to decrease in $K E$ of $A$ .

answer is A, C, D.

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Detailed Solution

Momentum of the system is conserved as external force acting on the system is zero.

Some heat is also dissipated .

After initial slipping , the objects will finally acquire a common velocity v. Let l be the displacement of A relative to B and x be the displacement of B relative to ground . If f be the force of friction between A and B , then by work energy theorem ,

for A, f $(l + x) = \frac{1}{2} m_{A} {(v_{0})}^{2} - \frac{1}{2} m_{A} v^{2}$ ………(1) and for B , fx = $\frac{1}{2} m_{B} v^{2} . . . . . . . . . . (2)$