Question

Three blocks, of masses $m_{1}=2.0,\, m_{2}=4.0$ and $m_{3}=6.0\, kg$ are connected by strings on a frictionless inclined plane of $60^{\circ}$, as shown $J$ the figure. A force $F=120$ $N$ is applied upward along the incline to the uppermost block, causing an upward movement of the blocks, if connecting cords are light. The values of tensions $T_{1}$ and in the cords are

• A. $T_{1}=20\,N,\,T_{2}=60\,N $
• B. $ T_{1}=60\,N,\,T_{2}=60\,N $
• C. $T_{1}=30\,N,\,T_{2}=50\,N $
• D. $T_{1}=20\,N,\,T_{2}=100\,N$

Answer 1

Answer: (A)

$T_{2}=\frac{\left(m_{1}+m_{2}\right) F}{\left(m_{1}+m_{2}+m_{3}\right)}$
$=\frac{(2+4) \times 120}{(2+4+6)}=\frac{6 \times 120}{12} T_{2}=60\, N$
$T_{1}=\frac{m_{1} F}{\left(m_{1}+m_{2}+m_{3}\right)}=\frac{2 \times 120}{12}$
$= 20\, N$