3 blocks of masses 2 kg , 3 kg and 5 kg are connected to each other with light string and are then p

Question

3 blocks of masses 2 kg , 3 kg and 5 kg are connected to each other with light string and are then placed on a smooth frictionless surface. See fig. below. Let the system be pulled with a force F from the side of lighter mass so that it moves with an acceleration of $1 \mathrm{~ms}^{-2} . \mathrm{T}_{1}$ and $\mathrm{T}_{2}$ denote the tensions in the other strings. The value of $F$ is\

Professor PC Thomas Classes · Answer

First 18:-\ Net force on 5 kg is $\mathrm{T}_{2}=\mathrm{ma}=5 	imes 1=5 \mathrm{~N}$\ Then 17:-\ Net force on $3 \mathrm{~kg}=\mathrm{T}_{1}-\mathrm{T}_{2}$ 
$ \begin{aligned} & \mathrm{T}_{1}-\mathrm{T}_{2}=3 	imes 1 \ & \begin{aligned} \mathrm{T}_{1}= & 3 	imes 1+\mathrm{T}_{2} \ = & 3 	imes 1+5 	imes 1=8 \mathrm{~N} \end{aligned} \end{aligned} $ 
Now 17 :-\ Net force on 2 kg is $\mathrm{F}-\mathrm{T}_{1}$
 $ \begin{aligned} \mathrm{F}-\mathrm{T}_{1} & =\mathrm{ma}=2 	imes 1 \ \mathrm{~F} & =2 	imes 1+8 	imes 1 \ & =10 \mathrm{~N} \end{aligned} $