Answer with Explanation:
We are given that
[tex]m_1=20 kg[/tex]
[tex]m_2=30 kg[/tex]
We have to find the acceleration of the system and the tension in the string.
[tex]30g-T=30a[/tex]...(1)
[tex]T-20g=20a[/tex]
[tex]T=20a+20g[/tex]...(2)
Using equation (2) in equation (1)
[tex]30g-(20a+20g)=30a[/tex]
[tex]30g-20a-20g=30a[/tex]
[tex]10g=30a+20a=50a[/tex]
[tex]a=\frac{10g}{50}=\frac{10\times 9.8}{50}=1.96 m/s^2[/tex]
Where [tex]g=9.8m/s^2[/tex]
Using the value of a in equation (2)
[tex]T=20(a+g)=20(1.96+9.8)=235.2 N[/tex]
Acceleration of the system is 1.96 m/s² and the tension in the string is 235.2 N
For 30 kg of weight
30g - T = 30a ....... Eq1
For 20 kg of weight
T - 20g = 20a ....... Eq2
From Eq 2 and Eq 1
50a = 10g
a = 10g / 50
a = (10)(9.8) / 50
a = 98 / 50
Acceleration = 1.96 m/s²
So,
T - 20g = 20a
T - 20(9.8) = 20(1.96)
T = 20(9.8) + 20(1.96)
Tension = 235.2 N
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