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Correct option is A)

$Mu=Mv_{1}+2Mv_{2} $_____ (i)

and $21 Mu_{2}=21 Mv_{1}+21 2M v_{2}$_____ (ii)

Solving (i) and (ii)

$v_{2}=34 u$

$v_{2}=34 u$

Similarly for second and third ball

$2M ×34 u=2M v_{2}+2_{2}M v_{3}$

$2M ×34 u=2M v_{2}+2_{2}M v_{3}$

and $21 2M (34 u)_{2}$$=21 2M (v_{2})_{2}+21 (2)_{2}M (v_{3})_{2}$

Solving $v_{3}=(a_{r} )u$

in this way, $v_{n}=(34 )_{n−1}u$

For nth ball to loop $v_{n}=5gR $

i.e.,$(34 )_{n−1}u=5gR $

or $u=(43 )_{n−1}5gR $

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