Question:
Three masses are connected (as Shown) on a horizontal frictionless surface and pulled by a force of 60 N. The tensions \({{T}_{1}}\) and \({{T}_{2}}\) are in the ratio
Three masses are connected (as Shown) on a horizontal frictionless surface and pulled by a force of 60 N. The tensions \({{T}_{1}}\) and \({{T}_{2}}\) are in the ratio
Updated On: Jul 26, 2023
- $ 1:1 $
- $ 1:5 $
- $ 1:4 $
- $ 4:5 $
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The Correct Option is B
Solution and Explanation
: Horizontal component of force $ =60\text{ }cos30{}^\circ $ $ =30N $ Acceleration of system $ a=\frac{force}{(3+12+15)} $ $ =\frac{30}{30}=1\,m/{{s}^{2}} $ $ \therefore $ $ {{T}_{2}}= $ mass pulled x acceleration $ =(3+12)\times 1=15N $ $ {{T}_{1}}=3\times 1=3N $ $ \therefore $ $ \frac{{{T}_{1}}}{{{T}_{2}}}=\frac{3}{15}=\frac{1}{5} $
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Concepts Used:
Tension
A force working along the length of a medium, especially if this force is carried by a flexible medium like cable or rope is called tension. The flexible cords which bear muscle forces to other parts of the body are called tendons.
Net force = 𝐹𝑛𝑒𝑡 = 𝑇−𝑊=0,
where,
T and W are the magnitudes of the tension and weight and their signs indicate a direction, be up-front positive here.
Read More: Tension Formula