Question

A metre rod of mass 200 g is suspended by two strings at each end as shown in figure. A body of mass 300 g is suspended by a weightless string at 30 cm mark. The tensions in the string 2 is

• A. 6.6 N
• B. 1.9 N
• C. 1.3 N
• D. 2 N

Answer 1

Answer: (B)

1.9 N

Answer 2

The various forces acting on the metre rod are shown in figure. Net force acting on the rod is zero. That is, $T_1 + T_2 - Mg - mg = 0$ or $T_1 + T_2 = (M + m) g$ [ $\therefore$ g = 10 m $s^{-1}$ = (0.3 + 0.2) $\times$ 10 N = 0.5 $\times$ 10 N = 5 N ....(1) $\therefore$ Net torqure acting on the rod = $T_2 \times (1.00 \, m ) - Mg \times (0.3 \, m) - mg \times (0.5 \, m)$ For equilibrium, net torque acting on the body is zero $\therefore$ $T_2 \times (1.00 \, m ) - Mg \times (0.5) - mg \times (0.5 \, m) = 0$ i.e. $T_2 = mg \times 0.5 +Mg \times 0.3 = 0.2 \times 10 \times 0.5 + 0.3 \times 10 \times 0.3$ = 1 + 0.9 = 1.9 N