# Direction of tension in case of a rod

Masses A and B are connected by a light rod

In this question, we are supposed to find the direction of tension by the rod on the masses A and B. I did not understand why we have tension by rod on B in the direction along the rod and tension by rod on A in the direction opposite to the rod? While usually in the case of a string, we tend to take the direction of tension away from the object to which the string is connected.

Here is the full question:

Two small balls 'A' and 'B' of masses 0.3 kg and 0.6 kg respectively are rigidly attached to the ends of a light rigid rod of length R√2 and placed inside a fixed smooth spherical cavity of radius R = 0.5 m with the ball 'B' is located at the lowest point of cavity as shown in the figure. Immediately after the rod is released from rest. The normal force on the ball 'A' due to surface of cavity is X newton and the normal force on the ball 'B' due to surface of cavity is Y newton. (Take g = 10 m/s²)

The force exerted by the rod on A or B must act along the line of the rod i.e. along the line joining A and B. If the rod is in tension then it will pull A towards B, and B towards A. If the rod is in compression then it will push A in the opposite direction to B, and it will push B in the opposite direction to A - this is where a rod differs from a string, which can only be in tension and never in compression.

In either case, the force exerted by the rod on A must be equal in magnitude and opposite in direction to the force exerted by the rod on B. This is because Newton's Third Law tells us that whatever force the rod exerts on A, then A will exert an equal and opposite reaction force on the rod - and the same goes for B. If the forces exerted on A and B were not equal in magnitude then the reaction forces would not net to zero and there would be a non-zero net force on the rod. But we are told that the rod is "light" i.e. we can treat it as having zero mass - in which case the net force acting on the rod must also be zero.

• So how will we know if it is a case of compression or tension and how will decide the direction?
– user372994
Aug 2, 2023 at 15:39
• @AayushSethia The direction of the force exerted by the rod on A and B must be along the line joining A and B. The magnitude of the force, and whether it is tension or compression, will depend on the dynamics of the situation - how are A and B moving - and what other forces are acting on A and B. Your question does not include enough information to determine this. Aug 2, 2023 at 20:40
• Please tell me the direction as now I have modified the question
– user372994
Aug 5, 2023 at 3:19
• @AayushSethia From the geometry of the question you can see that the line joining A and B is at 45 degrees to the vertical, so the force exerted by the rod is along this line. You can also tell that the rod is in compression, so the force it exerts on A must be upwards and to the left - this is because the vertical component of this force on A must be equal and opposite to A's weight, and its horizontal component must be equal and opposite to the normal force exerted by the sphere on A, which is horizontal and to the right. Aug 5, 2023 at 8:43
• Thank you very much now I have understood the answer.
– user372994
Aug 6, 2023 at 12:19