A spring of spring constant 5 × 10³ N/m is stretched initially by 5cm from the unstretched position. Then the work required to stretch it further by another 5 cm is

a) 12.50 N-m

b) 18.75 N-m

c) 25.00 N-m

d) 6.25 N-m

To calculate the work required to stretch the spring further by another 5 cm, we will use the formula for the work done in stretching a spring:

W = (1/2) k (x2² - x1²)

Where:

W = Work done
k = Spring constant (given as 5 × 10³ N/m)
x1 = Initial displacement (5 cm = 0.05 m)
x2 = Final displacement (Initial displacement + additional displacement = 0.05 m + 0.05 m = 0.10 m)
Step 1: Write the formula
W = (1/2) × k × (x2² - x1²)

Step 2: Substitute the values
W = (1/2) × 5000 × (0.10² - 0.05²)
W = 0.5 × 5000 × (0.01 - 0.0025)
W = 2500 × (0.0075)

Step 3: Calculate
W = 2500 × 0.0075
W = 18.75 N-m

Final Answer: (b) 18.75 N-m