What is Tension in a String? Massless String Assumption

Physics · Laws Of Motion · NEET

Tension is the pulling force that a stretched string, rope, or thread applies on the body tied to its ends. It always pulls the body toward the string, along the string, and it is the same at every point of a massless (light) string. Memory hook: a string can only PULL, never PUSH, and a light string carries the same pull from one end to the other.
Massless string: same tension T everywhere; string can only pullmT (pulls up)mgT at top pointT at lower pointT (top) = T (lower)(true because string mass = 0)
Left: a light string pulls the hanging block upward with tension T; at rest T = mg, but if the block accelerates use T = m(g±a). Right: because the string is massless, tension has the same value T at every point along it.

Your doubts, answered

Does tension pull the body or push it? Which direction does it act?

Tension can only PULL, never push. A string cannot push a body away (a rope goes slack if you try). So tension on any body always acts AWAY from the body, along the string, toward the point where the string is attached or over the pulley. When you draw a free body diagram, the tension arrow on the block points along the string, away from the block.

Is tension the same at every point of the string?

For a massless (light) string it is. NCERT tells you to 'neglect the mass of the string'. When mass = 0, Newton's second law on any small piece gives T2 - T1 = (mass)(a) = 0, so T1 = T2. That is why one symbol T works for the whole string. If the string had real mass, tension would be larger near the top of a hanging string (it holds more weight below it).

Why do we assume the string is massless and inextensible?

Two reasons for NEET. Massless (light): so tension is the same throughout and the string itself needs no force to accelerate, which keeps the maths clean. Inextensible: it does not stretch, so both connected bodies have the SAME magnitude of acceleration and the SAME speed. These two assumptions are what let you solve pulley and connected-block problems with one value of T and one value of a.

Is the tension always equal to the weight of the hanging body?

Only when the body is in equilibrium (at rest or moving at constant velocity). Then T = mg. If the body accelerates, T is NOT mg. For a body pulled up with acceleration a, T = m(g + a). For a body going down with acceleration a, T = m(g - a). Always write Newton's second law along the string instead of assuming T = mg.

What is the difference between tension and normal reaction?

Both are contact forces, but tension comes from a stretched string and always PULLS along the string. Normal reaction comes from a surface pressing on a body and always PUSHES perpendicular (normal) to the surface. A string pulls; a surface pushes.

⚠️ The NEET trap
Tension in the string holding a body in a lift always equals mg.
Tension equals mg only when the lift (and body) is at rest or moving at constant speed. If the lift accelerates up, T = m(g + a); if it accelerates down, T = m(g - a). Always apply F = ma along the string.
🧠 See a string and a moving/accelerating body? Do not write T = mg by reflex. Write Newton's second law first.

Real NEET questions

2017

One end of a string of length l is connected to a particle of mass m and the other end to a small peg on a smooth horizontal table. If the particle moves in a circle with speed v, the net force on the particle (directed towards the centre) is (T = tension in the string):

A · T
B · T − mv²/l
C · T + mv²/l
D · Zero
Solution: The only horizontal force on the particle is the tension T pulling it toward the centre (the table is smooth, so no friction; weight and normal reaction are vertical and cancel). The net inward force is therefore just T. It is a trap to add or subtract mv²/l: the quantity mv²/l is the REQUIRED centripetal force, and here that requirement is met by T itself, so T = mv²/l. The net force IS the tension T. Correct option: A.
2017

Two blocks A and B of masses 3m and m are connected by a massless inextensible string and the whole system hangs from a massless spring. The magnitudes of the accelerations of A and B immediately just after the string is cut are, respectively:

A · g, g/3
B · g/3, g
C · g, g
D · g/3, g/3
Solution: Before cutting: the string tension holds B, so T = mg. The spring holds both blocks, so spring force = 3mg + mg = 4mg. The instant the string is cut, the spring force cannot change instantly, so it is still 4mg upward on A. For A (mass 3m): net force = 4mg − 3mg = mg upward, so a_A = mg / 3m = g/3. For B (mass m): the string is gone, only gravity acts, so a_B = g downward. Answer: A has g/3, B has g. Correct option: B.

Solved Laws Of Motion NEET PYQs

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Frequently asked

What is tension in a string in simple words?

Tension is the pulling force inside a stretched string that it applies on the bodies tied to its ends. It pulls each body inward along the string. Its SI unit is the newton (N).

Why is tension the same throughout a massless string?

Because a massless string needs zero force to accelerate. Newton's second law on any piece gives T2 - T1 = mass × a = 0, so the tension has one value everywhere. This only works when we neglect the string's mass, as NCERT does.

Can tension be negative or zero?

Tension is never negative because a string cannot push. It can be zero when the string goes slack (loses its stretch), for example at the top of a vertical circle when the speed drops to the minimum value.

Is tension a contact force or a field force?

Tension is a contact force. It acts only through the physical string that touches the body. It is not a field force like gravity, which acts at a distance.

How is tension different for an inextensible versus a stretchy string?

For an inextensible (non-stretching) string, both connected bodies share the same acceleration and speed, which is what NEET problems assume. A real stretchy string would allow different motions and store energy, making it far harder to solve.