First slide

Stress and strain

Question

A block of mass 50 kgk is suspended by two strings 1 and 2 as shown in figure. The strings are of same length. Cross sectional area and young's modulus of the string 1 are A and Y and those of string 2 are 2A and 2Y respectively. If the block always remains horizontal, tension induced in string 1 is

Moderate

A

100 N
B

250 N
C

200 N
D

300 N

Solution

Elongation produced in 1 = Elongation produced in 2
$\begin{array}{l} \Rightarrow \frac{T_{1} . l}{A_{1} . Y_{1}} = \frac{T_{2} . l}{A_{2} l_{2}} \Rightarrow \frac{T_{1}}{T_{2}} = \frac{A_{1}}{A_{2}} . \frac{Y_{1}}{Y_{2}} = \frac{1}{2} . \frac{1}{2} \\ \Rightarrow \frac{T_{1}}{T_{2}} = \frac{1}{4} . ....... (1) \end{array}$
Also, $T_{1} + T_{2} = 500 N . ........ (2)$
Solving, $T_{1} = 100 N$

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