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In procedure 1, cart 1 and cart 2 are initially at rest, and after the explosion the momentum of the two carts was the same.
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Answer #1

here,

when the carts are initially at rest

after the explosion

the momentum of the cart is conserved for the system

and the initial momentum is equal to the final momentum

and this is same for initial moving cart

the initial momentum of carts is equal to the final momentum of the carts after the collison

just the magnitude of initial momentum is different from the case when they are at rest

so, corrcet option is a) YES

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