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A two-meter-long rod is suspended with the help of two wires of equal length. One wire is of steel and its cross-section is $0.1 \mathrm{cm}^{2}$ and another wire is of brass and its cross-section area is $0.2 \mathrm{cm}^{2}$. If a load $\mathrm{W}$ is suspended from the rod and introduced in both the wires is same then the ratio of tensions in them will be
(a) will depend on the position of $\mathrm{W}$
(b) $\mathrm{T}_{1} / \mathrm{T}_{2}=2$
(c) $\mathrm{T}_{1} / \mathrm{T}_{2}=1$
(d) $\mathrm{T}_{1} / \mathrm{T}_{2}=0.5$

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Last updated date: 27th Feb 2024
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IVSAT 2024
Answer
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Hint: We know that tension is nothing but the drawing force acting on the body when it is hung from objects like chain, cable, string etc. It is represented by T. The direction of tension is the pull which is given the name tension. Thus, the tension will point away from the mass in the direction of the string or rope. In case of the hanging mass, the string pulls it upwards, so the string or rope exerts an upper force on the mass and the tension will be on the upper side. The tension force is the force that is transmitted through a string, rope, cable or wire when it is pulled tight by forces acting from opposite ends. The tension force is directed along the length of the wire and pulls equally on the objects on the opposite ends of the wire. Based on this concept we have to solve this question.

Complete step by step answer
We know that momentum is a physics term that refers to the quantity of motion that an object has. A sports team that is on the move has the momentum. If an object is in motion (on the move) then it has momentum. One example is the use of air bags in automobiles. Air bags are used in automobile.s because they are able to minimize the effect of the force on an object involved in a collision. Air bags accomplish this by extending the time required to stop the momentum of the driver and passenger. Momentum is mass in motion, and any moving object can have momentum. An object's change in momentum is equal to its impulse. Impulse is a quantity of force times the time interval. Impulse is not equal to momentum itself; rather, it's the increase or decrease of an object's momentum.
We should know that linear momentum is defined as the product of a system's mass multiplied by its velocity. Momentum is directly proportional to the object's mass and also its velocity. Thus, the greater an object's mass or the greater its velocity, the greater its momentum. Note that the linear moment is a vector quantity and is conserved in any direction. In the center-of-mass system, the total momentum is always zero, before and after the interaction, in any direction. Angular momentum is inertia of rotation motion. Linear momentum is inertia of translation motion. The big difference is that the type of motion which is related to each momentum is different. It is important to consider the place where the force related to rotation applies, which is appears as 'r' in the formula
$\mathrm{A}_{\mathrm{S}}=0.1 \mathrm{cm}^{2}$
$\mathrm{A}_{\mathrm{B}}=0.2 \mathrm{cm}^{2}$
$\mathrm{T}_{1} \mathrm{x}=\mathrm{T}_{2} \cdot(\mathrm{l}-\mathrm{x})$
Here 'x' is not given, so it will depend on the position of W.

So, option A is correct.

Note: We should know that the weight of an object may be thought of as acting at a single point called its centre of mass. Depending on the object's shape, its centre of mass can be inside or outside it. The weight of an object and its mass are directly proportional. The centre of mass of an object is the point at which the object can be balanced. The centre of mass is useful because problems can often be simplified by treating a collection of masses as one mass at their common centre of mass. The weight of the object then acts through this point. In the human form the centre of mass has no fixed point but is dependent on the position of the performer at any given time. Due to the body composition the centre of mass of all athletes varies, as bone, fat, tissue and muscle all contribute to total mass and are in different proportions in each performer.