NEET Work Energy and Power — Set 6

Question 1

A force $ F = 10x^2 \, \text{N} $ acts from $ x = 0 $ to $ x = 1 \, \text{m} $. What is the work done?

Accepted Answer

Work $ W = \int_0^1 10x^2 \, dx = \left[ \frac{10}{3} x^3 \right]_0^1 = \frac{10}{3} \times 1 = \frac{10}{3} \approx 3.33 \, \text{J} $.

Question 2

A spring with constant $ k = 200 \, \text{N/m} $ is compressed by $ 0.1 \, \text{m} $. What is the potential energy stored in the spring?

Accepted Answer

Potential energy $ V = \frac{1}{2} k x^2 $. $ V = \frac{1}{2} \times 200 \times (0.1)^2 = 100 \times 0.01 = 1 \, \text{J} $.

Question 3

A $ 8 \, \text{kg} $ mass is lifted $ 4 \, \text{m} $ in $ 2.5 \, \text{s} $ at constant speed. What is the power? (Take $ g = 10 \, \text{m/s}^2 $)

Accepted Answer

Work $ W = mgh = 8 \times 10 \times 4 = 320 \, \text{J} $. Power $ P = \frac{W}{t} = \frac{320}{2.5} = 128 \, \text{W} $.

NEET Physics: Work Energy and Power — Practice Set 6