1 \includegraphics[max width=\textwidth, alt={}, center]{3e8248ca-74f1-443f-a5db-d7da532d2815-2_435_665_255_699} A small object \(W\) of weight 100 N is attached to one end of each of two parallel light elastic strings. One string is of natural length 0.4 m and has modulus of elasticity 20 N ; the other string is of natural length 0.6 m and has modulus of elasticity 30 N . The upper ends of both strings are attached to a horizontal ceiling and \(W\) hangs in equilibrium at a distance \(d \mathrm {~m}\) below the ceiling (see diagram). Find \(d\).

## Question 1:

| Answer | Marks | Guidance |
|--------|-------|----------|
| Use of $T = \frac{\lambda e}{l}$ | M1 | Attempt at one tension; allow use of $x$; allow $2l$ for M1 |
| $\frac{20(d-0.4)}{0.4}$ or $\frac{30(d-0.6)}{0.6}$ | A1 | Either term seen, accept in terms of $x$ |
| Weight = tension 1 + tension 2 | M1 | Condone $Wg$ and $W/g$ |
| $100 = 50d - 20 + 50d - 30$ | A1 | Fractions and brackets removed |
| $(AW =)\ 1.5$ (m) | A1 | |
| **[5]** | | |

1\\
\includegraphics[max width=\textwidth, alt={}, center]{3e8248ca-74f1-443f-a5db-d7da532d2815-2_435_665_255_699}

A small object $W$ of weight 100 N is attached to one end of each of two parallel light elastic strings. One string is of natural length 0.4 m and has modulus of elasticity 20 N ; the other string is of natural length 0.6 m and has modulus of elasticity 30 N . The upper ends of both strings are attached to a horizontal ceiling and $W$ hangs in equilibrium at a distance $d \mathrm {~m}$ below the ceiling (see diagram). Find $d$.

\hfill \mbox{\textit{OCR M3 2013 Q1 [5]}}