Three blocks m1,m2, and m3 are arranged as shown in figure. If m2=5kg and m3=8kg then the mass of block m1 for which the 8 kg block remains at rest is p3kg . The value of p is…

Here, T0=8g=80NAlso,T0=2T ⇒T=40NFrom force diagram of 5 kg block 50−T−5a50−40−5a10=5aa=2ms−2From force diagram of m1T−m1g=m1a or 40−m1g=m1×2 or 40=10m1+2m1=12m1∴m1=4012=103kg

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Three blocks $m_{1}, m_{2}, and m_{3}$ are arranged as shown in figure. If $m_{2} = 5 kg and m_{3} = 8 kg$ then the mass of block m₁ for which the 8 kg block remains at rest is $\frac{p}{3} kg$ . The value of p is…

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Detailed Solution

Here, $T_{0} = 8 g = 80 N$

$Also, T_{0} = 2 T$ $\Rightarrow T = 40 N$
From force diagram of 5 kg block

$\begin{aligned} 50 - T - 5 a \\ 50 - 40 - 5 a \\ 10 = 5 a \\ a = 2 {ms}^{- 2} \end{aligned}$
From force diagram of m₁

$\begin{array}{l} T - m_{1} g = m_{1} a \\ or 40 - m_{1} g = m_{1} \times 2 \\ or 40 = 10 m_{1} + 2 m_{1} = 12 m_{1} \\ ∴ m_{1} = \frac{40}{12} = \frac{10}{3} kg \end{array}$