Laws of Motion 2 Question 5
5. Two blocks of mass $2.9 kg$ and $1.9 kg$ are suspended from a rigid support $S$ by two inextensible wires each of length $1 m$ (see figure). The upper wire has negligible mass and the lower wire has a uniform mass of $0.2 kg / m$. The whole system of blocks, wires and support have an upward acceleration of $0.2 m / s^{2}$. The acceleration due to gravity is $9.8 m / s^{2}$.
$(1989,6 M)$
(a) Find the tension at the mid-point of the
lower wire.
(b) Find the tension at the mid-point of the upper wire.
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Answer:
Correct Answer: 5. (c)
Solution:
- Free body diagram of pulley is $T=M g$ shown in figure. Pulley is in equilibrium under four forces. Three forces as shown in figure and the fourth, which is equal and opposite to the resultant of these three forces, is the force applied
by the clamp on the pulley (say $F$ ).
Resultant $R$ of these three forces is
$$ R=\left(\sqrt{(M+m)^{2}+M^{2}}\right) g $$
Therefore, the force $F$ is equal and opposite to $R$ as shown in figure.
$\therefore F=\left(\sqrt{(M+m)^{2}+M^{2}}\right) g$
