Question

The identical bodies A, B, and C each of mass 2kg, tied to an inextensible and massless string passing over a smooth pulley as shown in the figure. The tension in string connecting B to C will be:

• A. 13 N
• B. 0.13 N
• C. 3.3 N
• D. zero

Answer 1

The correct option is A 13 N

Let the tension between body B and C is $T_1$,

The tension between body A and B is T${}_2$ ( because Pulley is smooth ) and 'a' is system acceleration

From FBD of Body C is shown in figure 1

mg - $T_1$ = ma ........ 1

From FBD of Body B is shown in figure 2

mg + $T_1$ - $T_2$ = ma ............2

From FBD of Body A is shown in figure 3

$T_2$ - mg = ma ............3

Add equation 2 and 3

$\therefore$ $T_1$ = 2 ma

put ma= $\frac{T_1}{2}$ in equation 1

mg - T${}_1$= $\frac{T_1}{2}$

$\therefore$ $T_1$ = 2 $\frac{mg}{3}$

put m= 2 Kg ; g= 9.8

$T_1$= 13.067 N $\simeq$ 13 N