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Tension in a String

Three equal w...

Question

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

Zero

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13 N

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3.3 N

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19.6 N

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Solution

The correct option is B $13 N$
Taking blocks A, B, C and the connected strings as a system,

Acceleration of system
$a = \frac{Net pulling force}{Total mass} = \frac{4 g - 2 g}{6} = \frac{g}{3}$
Equation of motion of block $C$ is
$m_{c} g - T_{B C} = m_{c} a$
$∴ T_{B C} = m_{c} (g - a)$
$= 2 (9.8 - \frac{9.8}{3}) = 13 N$

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

The correct option is B 13 NTaking blocks A, B, C and the connected strings as a system, Acceleration of system a=Net pulling forceTotal mass=4g−2g6=g3 Equation of motion of block C is mcg−TBC=mca ∴TBC=mc(g−a) =2(9.8−9.83)=13 N

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