Question

A block of mass $M$ is attached to the lower end of a vertical rope of mass $m$. An upward force $P$ acts on the upper end of the rope. The system is free to move. The force exerted by the rope on the block is $\frac{PM}{M+m}$.

• A. In all cases
• B. Only if the rope is uniform
• C. In gravity-free space only
• D. Only if $P>(M+m)g$

Answer 1

Answer: (D)

Only if $P>(M+m)g$

$P-T_1=0\times a=0$P = T_{1}T_{1} - mg - T_{2} = ma\dfrac {T_{2} - Mg = Ma}{P - (M + m) g = (M + m)a}\therefore a = \dfrac {P - (M + m)g}{(M + m)}T_{2} = Mg + Ma= Mg + \dfrac {M[P - (M + m)g]}{(M + m)}= \dfrac {M^{2}g + Mmg + MP - M^{2}g - Mmg}{M + m}= \dfrac {MP}{M + m}$.Onlyif$P > (M + m)g$, one can have acceleration and this derivation will be valid.