A) (a)\[F\left( 1-\frac{l}{L} \right)\]
B) \[2F\left( 1-\frac{l}{2L} \right)\]
C) \[\frac{F}{L}\]
D) \[\frac{F}{l}\left( 1-\frac{l}{L} \right)\]
Correct Answer: A
Solution :
[a] Let a be the acceleration of the rope and M be its total mass. Then \[T=\frac{M}{L}\left( L-l \right)a\] ?.(i) \[\text{and }F-T=\frac{M}{L}\times \ell a\] ?(ii) Dividing (i) and (ii), \[\frac{F-T}{T}=\frac{\ell }{L-\ell }\Rightarrow F(L-\ell )-T(L-\ell )=T\ell \] \[\Rightarrow F(L-\ell )=T(L-\ell +\ell )=T\times L\] \[\Rightarrow T=F\left( 1+\frac{\ell }{L} \right)\]You need to login to perform this action.
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