In the above given problem if the lower thread is pulled with a jerk, what happens?

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Q. In the above given problem if the lower thread is pulled with a jerk, what happens?

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Concept understanding — Tension in Connected Bodies

Tension in Connected Bodies – A First Look

Imagine you and a friend are pulling a heavy box across the floor using a single rope between you. You pull one end, your friend pulls the other. The rope goes taut. What do you feel in your hands? A pull — that's tension. Now imagine the box is on a frictionless surface and you pull harder. The rope stays taut, the box accelerates, and the pull you feel is still there, but now it's doing something more: it's transmitting your force to the box.

That's the core idea. Tension is the internal force that runs through a string, rope, or cable when it is stretched. In problems with connected bodies, the string links two or more masses together, and the tension force is the same at every point along a massless, inextensible string. It pulls equally on both ends — on each body it acts along the string, toward the string's centre.

Important

For a massless, inextensible string, tension is uniform throughout its length. That means the magnitude of the force on mass A is exactly the same as the magnitude of the force on mass B.

Why does tension exist?

When you pull one end of a string, the string stretches microscopically. The molecules resist being pulled apart, and that resistance is what we call tension. In ideal physics problems, we ignore the stretch and the mass of the string itself. That simplification lets us say: the string is just a perfect force transmitter — it takes the force from one body and delivers it unchanged to the other.

The key step: Isolate each body

To find the tension, you cannot just look at the whole system. You must apply Newton's second law ( $F = ma$ ) to each body separately. Draw a free-body diagram for each mass. On each diagram, the tension force appears as an arrow pointing away from the body along the string (because the string pulls inward on each mass).

Here is the general procedure:

Identify all bodies connected by the string.
Assume the string is taut and inextensible — all bodies move with the same acceleration magnitude.
Choose a direction of motion (positive direction) for the whole system.
For each body, write $F_{\text{net}} = m a$ , including tension as one of the forces.
Solve the equations simultaneously.

Tip

If the string passes over a frictionless, massless pulley, the tension is the same on both sides of the pulley. The pulley only changes the direction of the tension force, not its magnitude.

A simple example to make it concrete

Consider two blocks on a frictionless horizontal surface. Block A (mass $m_1$ ) is tied by a string to block B (mass $m_2$ ). You pull block B with a horizontal force $F$ .

On block A: the only horizontal force is tension $T$ pulling it forward. So $T = m_1 a$ .
On block B: the horizontal forces are $F$ forward and $T$ backward. So $F - T = m_2 a$ .

Since the string is inextensible, both blocks have the same acceleration $a$ . Add the two equations:

T + (F - T) = m_1 a + m_2 a \quad \Rightarrow \quad F = (m_1 + m_2)a

So $a = \frac{F}{m_1 + m_2}$ . Then from $T = m_1 a$ , you get:

T = \frac{m_1}{m_1 + m_2} F

Notice: tension is not equal to the applied force $F$ . It is only a fraction of it, determined by the mass ratio. If $m_1$ is very small, tension is small — the string barely pulls the light block. If $m_1$ is huge, tension is nearly $F$ — the heavy block resists acceleration, so the string must pull hard.

Watch out

A common mistake is to think tension equals the applied force. It does not. Tension is whatever force is needed to accelerate the other block at the same rate as the whole system.

What about vertical motion? (Atwood machine) …

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A sudden jerk on the lower thread applies a large impulsive force over a very short time, causing the lower thread to break before the inertia of the block can transmit the force to the upper thread. The block remains intact, and the upper thread stays unbroken.

The key concept here is inertia — the tendency of a body to resist a change in its state of motion. When you pull a thread slowly, the force is transmitted gradually through the block, allowing both threads to experience similar tension. But when you pull with a jerk (a sudden, sharp pull), the time of application is extremely short. The block, due to its inertia, does not have time to accelerate and transfer the force to the upper thread. Instead, the lower thread bears the entire impulsive force and snaps.

Let’s break this down step by step.

Setup of the problem

Imagine a block of mass $m$ suspended from a ceiling by an upper thread. A lower thread is attached to the bottom of the block. Both threads are identical in material and thickness. You pull the lower thread downward.
Slow pull — the usual case

If you pull the lower thread slowly, the force increases gradually. The block accelerates downward slightly, and the tension in the upper thread increases to balance the weight plus the pull. Both threads experience nearly equal tension (since the block’s acceleration is small), so either thread may break depending on which is weaker — but typically both are equally stressed.
Jerk — the sudden pull

When you pull with a jerk, the force is applied over a very short time interval $\Delta t$ . The impulse delivered is $F \Delta t$ , which equals the change in momentum of the lower thread’s end. The block, being massive, has large inertia — it cannot gain significant velocity in that tiny $\Delta t$ . So the lower thread experiences a huge tension spike, while the upper thread feels almost nothing because the block hasn’t moved yet.
Why the lower thread breaks

The tension in the lower thread rises to a value far above its breaking strength almost instantly. The upper thread, however, still only supports the weight of the block (plus a negligible extra due to the block’s tiny acceleration). So the lower thread snaps, and the block remains hanging from the upper thread. …

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Q.In the above given problem if the lower thread is pulled with a jerk, what happens?

Concept understanding — Tension in Connected Bodies

Tension in Connected Bodies – A First Look

Why does tension exist?

The key step: Isolate each body

A simple example to make it concrete

What about vertical motion? (Atwood machine) …

Concept: Inertia Under an Impulsive Force

Q.In the above given problem if the lower thread is pulled with a jerk, what happens?

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