Question

K= 1000 N/m
In the arrangement shown in the figure pulley is light and smooth. The
extension in the spring (g=10m/s)
(A1.33 cm
(B) 1 cm
(C) 1.67 cm
(D) 2 cm
​

Answer 1

Given:

A simple pulley weight and spring system has been provided as shown in the diagram. The Spring Constant is 1000 N/m .

To find:

Extension in the spring.

Calculation:

Considering the spring force to be analogous to tension present in wires :

For the 2 kg mass :

$2g - (kx) = 2a \: \: ........(1)$

For the 1 kg mass :

$(kx) - 1g = 1a \: \: ..........(2)$

Adding the two equations :

$= >2g - 1g = 2a + 1a$

$= > 1g = 3a$

$= > a = \dfrac{g}{3}$

Putting value of "a" in eq. (1) :

$\therefore \: 2g - (kx) = 2a$

$= > \: 2g - (kx) = 2 \times ( \dfrac{g}{3} )$

$= > kx = 2g - \dfrac{2g}{3}$

$= > kx = \dfrac{4g}{3}$

$= > x = \dfrac{4g}{3k}$

Converting metres to cm :

$= > x = \dfrac{4g \times 100}{3k} \: cm$

$= > x = \dfrac{4 \times 10\times 100}{3 \times 1000} \: cm$

$= > x = \dfrac{4}{3} \: cm$

$= > x = 1.33 \: cm$

So final answer is :

$\boxed{ \large{ \bold{x = 1.33 \: cm}}}$