Question

A block of weight $W$ produces an extension of $9cm$ when it is hung by an elastic spring of length $60cm$ and is in equilibrium. The spring is cut into two parts, one of length $40cm$ and the other of length $20cm$. The same load $W$ hangs in equilibrium supported by both parts as shown in the figure. The extension now is:

• A. $9cm$
• B. $6cm$
• C. $3cm$
• D. $2cm$

Answer 1

The correct option is A $9cm$

$W=kx=9k$

Spring constant is inversely proportional to length

Initial length=60cm

$k_1{l}_1=k_2{l}_2$

$k60=k_{1}20$

$k_1=3k$

$k60=k_{2}40$

$k_2=\frac{3}{2}k$

Now extension in both sittings is same

W=$(k_1+k_2)x=\frac{9}{2}kx=9k$

x=2 cm