Two identical spring balances S₁ and S₂ are connected one after the other and are held vertically as shown in the figure. A mass of 10 kg is hanging from S₂. If the readings on S₁ and S₂ are W₁ and W₂ respectively, then :
- (a)W₁ = 5 kg and W₂ = 10 kg
- (b)W₁ = 10 kg and W₂ = 5 kg
- (c)W₁ = 5 kg and W₂ = 5 kg
- (d)W₁ = 10 kg and W₂ = 10 kg
Correct — D, W₁ = 10 kg and W₂ = 10 kg. The two balances are joined in series, one below the other, and the 10 kg mass hangs from the lower one, S₂. A spring balance shows the tension in its own spring — the force pulling on its hook. S₂ directly supports the 10 kg load, so the tension in it, and hence its reading, is 10 kgf. S₁ hangs above S₂ and must support both the load and S₂; because the balances are treated as ideal, with their own weight neglected, the tension it carries is still the full 10 kgf. In a hanging series the same weight is transmitted through every link, so both balances read the same 10 kg.
- (a)W₁ = 5 kg and W₂ = 10 kg — This assumes the load is somehow shared or halved between the two balances. Series (one-below-the-other) balances do not split the weight — the same tension runs through both, so S₁ also reads the full 10 kg, not 5 kg.
- (b)W₁ = 10 kg and W₂ = 5 kg — The lower balance S₂ carries the 10 kg directly, so it cannot read only 5 kg. Both readings are 10 kg, not 10 and 5.
- (c)W₁ = 5 kg and W₂ = 5 kg — Halving the weight to 5 kg on each balance would be right only if the balances were side by side (in parallel), sharing the load. Here they are in series, so each carries the full 10 kg.
A spring balance measures the tension in its spring — the force pulling on its hook — which it displays as an equivalent mass in kilogram-force. When two balances hang one below the other (in series) and a weight hangs from the lower one, the same tension is transmitted up the whole chain, so both show the same reading, ignoring the balances' own weight.
The trap is to imagine the two balances sharing the load and each reading half. Sharing happens only when supports act in parallel, side by side. In a vertical series the tension is the same everywhere along the line, so each balance reports the full hanging weight.
- A spring balance reads the tension in its own spring, expressed as an equivalent mass (kilogram-force).
- For ideal, massless balances hung in series, the tension — and therefore the reading — is the same in each.
- Both S₁ and S₂ read 10 kg because the full 10 kg load is transmitted through both.
- Load is shared and halved only when supports act in parallel, not in series.
- Assuming series balances split the load and each reads half.
- Confusing series (one below the other) with parallel (side by side) supports.
- Forgetting that an ideal balance's own weight is neglected.
NDA sets up two spring balances or scales in series or parallel with a hanging mass and asks for each reading — decide whether the weight is transmitted (series, same reading) or shared (parallel, split).
No directly related past PYQ was found.
- practice — not a real PYQ
A 20 kg mass hangs from spring balance S₂, which itself hangs from spring balance S₁ above it. Ignoring the balances' weight, the readings are:
- (a)S₁ = 10 kg, S₂ = 20 kg
- (b)S₁ = 20 kg, S₂ = 20 kg
- (c)S₁ = 20 kg, S₂ = 10 kg
- (d)S₁ = 10 kg, S₂ = 10 kg
Answer(b) S₁ = 20 kg, S₂ = 20 kg — in a hanging series the same tension passes through both balances, so each reads the full 20 kg.
- practice — not a real PYQ
A 10 kg load is hung from a light rod supported at its two ends by two identical spring balances, one at each end (in parallel). If the load hangs at the midpoint, each balance reads about:
- (a)10 kg
- (b)5 kg
- (c)20 kg
- (d)0 kg
Answer(b) 5 kg — parallel supports share the load, so each carries about half of the 10 kg.