Question

Energy required to stretch a spring by 10 cm is 4 J, the spring constant of spring is
(1) 400 N/m
(2) 800 N/m
(3) 200 N/m
(4) 100 N/m​

Answer 1

Given :

፨ Energy required to stretch spring by 10cm (0.1m) = 4$\sf{J}$

To Find :

➝ We have to find spring constant of spring$.$

Solution :

⇒ Energy (U) required to stretch a spring of spring constant k by x m is given by

• U = 1/2 × kx²

⇒ U = 1/2 × kx²

⇒ 4 = 1/2 × k(0.1)²

⇒ 0.01k = 8

⇒ k = 800N/m

Answer 2

Given ,

Compression (x) = 10 cm or 0.1 m

Energy of spring (U) = 4 J

We know that , the energy of a spring is given by

$\boxed{ \sf{U = \frac{1}{2} k {(x)}^{2} }}$

Where ,

k = Spring or force constant

x = compression

Thus ,

4 = 1/2 × k × (0.1)²

8 = k × 1/100

k = 800 N/m

∴The correct option is (2) i.e 800 N/m