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  4. Three masses M =100 kg , m 1=10 kg and m 2=20 kg are arranged in a system as shown in figure. All the surfaces are frictionless and strings are inextensible and weightless. The pulleys are also weightless and frictionless. A force F is applied on the system so that the mass m 2 moves upward with an acceleration of 2 ms -2. The value of F is: (. Take .g =10 ms -2)

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Q. Three masses $M =100 \,kg , m _1=10\, kg$ and $m _2=20 \,kg$ are arranged in a system as shown in figure. All the surfaces are frictionless and strings are inextensible and weightless. The pulleys are also weightless and frictionless. A force $F$ is applied on the system so that the mass $m _2$ moves upward with an acceleration of $2\, ms ^{-2}$. The value of $F$ is :
$\left(\right.$ Take $\left.g =10\, ms ^{-2}\right)$Physics Question Image

JEE MainJEE Main 2022Laws of Motion

Solution:

Let acceleration of $100\, kg$ block $= a _1$
FBD of $100\, kg$ block w.r.t ground
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$F - T - N _1=100 a _1$
FBD of $20$ block wrt $100 \,kg$
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$ T -20 g =20(2)$
$ T =240 .....$(ii)
$N _1=20 a _1 \ldots \text {.... (iii) }$
FBD of $10\, kg$ block wrt $100\, kg$
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$ a_1=26 \, m / s ^2 $
$F -240-20(26)=100 \times 26$
$ \Rightarrow F =3360 \,N$