First slide

Connected bodies

Question

Three equal weights A, B, C of mass 2 kg each are hanging on a string passing over a fixed frictionless pulley as shown in the figure. The tension in the string connecting weights, B and C is:

Moderate

A

zero
B

13 N
C

3.3 N
D

19.6 N

Solution

For A: $T - 2 g = 2 a - - - - - (i)$
For B : $T_{1} + 2 g - T = - 2 a - - - - - (ii)$
For C : $2 g - T_{1} = 2 a - - - - (iii)$
Adding equations (i) and (ii),
we get $T_{1} = 4 a - - - - - (iv)$
From equations (iii) and (iv)
$2 g - 4 a = 2 a$
$a = \frac{g}{3} - - - - (v)$
From equations (iv) and (v),
$T_{1} = 4 \times \frac{g}{3} = 13 N$

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