A block of mass m is resting on a smooth horizontal surface. One end of a uniform rope of mass ( (m/3) ) is fixed to the block, which is pulled in the horizontal direction by applying force F at the other end. The tension in the middle of the rope is

Question

A block of mass m is resting on a smooth horizontal surface. One end of a uniform rope of mass ( (m/3) ) is fixed to the block, which is pulled in the horizontal direction by applying force F at the other end. The tension in the middle of the rope is (A)  (8/7)F  (B)  (1/7)F  (C)  (1/8)F  (D)  (1/5)F

Tardigrade Admin · Accepted Answer

Acceleration of the system a=(F/( m+(m)3 )) ∴ Tension in the middle of the rope t=( M+(M/6) )a Or T=(7m/6).(3F/4m) Or T=(7/8)F

Q. A block of mass $m$ is resting on a smooth horizontal surface. One end of a uniform rope of mass $(\frac{m}{3})$ is fixed to the block, which is pulled in the horizontal direction by applying force $F$ at the other end. The tension in the middle of the rope is

$\frac{8}{7} F$

$\frac{1}{7} F$

$\frac{1}{8} F$

$\frac{1}{5} F$

$\frac{7}{8} F$

Acceleration of the system
$a = \frac{F}{( m + \frac{m}{3} )}$
$∴$ Tension in the middle of the rope $t = (M + \frac{M}{6}) a$
Or $T = \frac{7 m}{6} . \frac{3 F}{4 m}$
Or $T = \frac{7}{8} F$

Q. A block of mass m is resting on a smooth horizontal surface. One end of a uniform rope of mass (3m​) is fixed to the block, which is pulled in the horizontal direction by applying force F at the other end. The tension in the middle of the rope is

78​F

71​F

81​F

51​F

87​F

Acceleration of the system a=(m+3m​)F​ ∴ Tension in the middle of the rope t=(M+6M​)a Or T=67m​.4m3F​ Or T=87​F