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Question
Two blocks of mass 5 kg and 3 kg are tied with a heavy rope of mass 2 kg. An external force of 200 N is applied on 5 kg block and the whole system accelerates upwards. Find the tension at the midpoint of the rope?
(Take g= 10 m/s2)
Two blocks of mass 5 kg and 3 kg are tied with a heavy rope of mass 2 kg. An external force of 200 N is applied on 5 kg block and the whole system accelerates upwards. Find the tension at the midpoint of the rope?
(Take g= 10 m/s2)
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Solution
The correct option is A 80 N
To calculate the total acceleration let us consider the entire setup to be a system of mass (5+2+3)=10 kg
FBD of the system will be
Using FBD, we can write
F−Mg=Ma
200−10×10=10×a
a=10 m/s2
The rope of mass 2 kg can be seen to be made up of two parts of 1 kg each, of equal length.
Now, the FBD of the lower part of the system will be
Using FBD, we can write T−4×g=4×a
T−4×10=4×10
⟹T=80 N
To calculate the total acceleration let us consider the entire setup to be a system of mass (5+2+3)=10 kg
FBD of the system will be
Using FBD, we can write
F−Mg=Ma
200−10×10=10×a
a=10 m/s2
The rope of mass 2 kg can be seen to be made up of two parts of 1 kg each, of equal length.
Now, the FBD of the lower part of the system will be
Using FBD, we can write T−4×g=4×a
T−4×10=4×10
⟹T=80 N
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