Hooke’s Law Numerical Questions [solved]

In this post, we will solve Numerical questions based on Hooke’s Law equation for spring.

Formula Used

If a force F produces extension x of the spring then:

k = F/x. Here, k = spring constant.

F = kx

x = F/k

Numerical Questions based on Hooke’s Law [solved]

Question 1] A spring is stretched 10 mm (0.01 m) by a weight of 2.0 N. Calculate: (a) the force constant k, and (b) the weight W of an object that causes an extension of 80 mm (0.08 m).

Solution:

a) k = F/x = 2/0.01 N/m = 200 N/m (answer)

b) Here, F = W.
k = 200 N/m (found above)
x=0.08 m

F =kx
=> W = kx
=>W = 200 x 0.08 N = 16 N

Question 2] What is the force constant of a spring which is stretched
a) 2 mm by a force of 4 N,
b) 4 cm by a mass of 200 g?

Solution:

a) x = 2 mm = 0.002 m
F = 4 N
k = F/x = 4/0.002 = 2000 N/m

b) x = 4 cm = 0.04 m

mass = 200 g = 0.2 kg
F = mg = 0.2 x 9.8 N = 1.96 N

k = F/x = 1.96/0.04 = 49 N/m