NEET Work Energy and Power — Set 18

Question 1

A $ 0.5 \, \text{g} $ drop falls from $ 600 \, \text{m} $ and hits the ground at $ 20 \, \text{m/s} $. What is the work done by the resistive force? (Take $ g = 10 \, \text{m/s}^2 $)

Accepted Answer

Work by gravity $ W_g = mgh = 0.0005 \times 10 \times 600 = 3 \, \text{J} $. Final $ K = \frac{1}{2} \times 0.0005 \times 20^2 = 0.1 \, \text{J} $. By work-energy theorem, $ K_f = W_g + W_r \Rightarrow 0.1 = 3 + W_r \Rightarrow W_r = -2.9 \, \text{J} $.

Question 2

A $ 0.9 \, \text{kg} $ object is dropped from $ 20 \, \text{m} $. What is its kinetic energy just before impact? (Take $ g = 10 \, \text{m/s}^2 $)

Accepted Answer

Potential energy $ V = mgh = 0.9 \times 10 \times 20 = 180 \, \text{J} $. By conservation, $ K_f = V_i = 180 \, \text{J} $.

Question 3

A force $ \mathbf{F} = 4\hat{\mathbf{i}} + 6\hat{\mathbf{j}} \, \text{N} $ acts on a particle moving along $ \mathbf{d} = -3\hat{\mathbf{i}} + 2\hat{\mathbf{j}} \, \text{m} $. What is the work done?

Accepted Answer

Work $ W = \mathbf{F} \cdot \mathbf{d} $. $ \mathbf{F} = 4\hat{\mathbf{i}} + 6\hat{\mathbf{j}} $, $ \mathbf{d} = -3\hat{\mathbf{i}} + 2\hat{\mathbf{j}} $. Scalar product: $ W = (4 \times -3) + (6 \times 2) = -12 + 12 = 0 \, \text{J} $.

NEET Physics: Work Energy and Power — Practice Set 18

Q1. A \( 0.5 \, \text{g} \) drop falls from \( 600 \, \text{m} \) and hits the ground at \( 20 \, \text{m/s} \). What is the work done by the resistive force? (Take \( g = 10 \, \text{m/s}^2 \))

Q2. A \( 0.9 \, \text{kg} \) object is dropped from \( 20 \, \text{m} \). What is its kinetic energy just before impact? (Take \( g = 10 \, \text{m/s}^2 \))

Q3. A force \( \mathbf{F} = 4\hat{\mathbf{i}} + 6\hat{\mathbf{j}} \, \text{N} \) acts on a particle moving along \( \mathbf{d} = -3\hat{\mathbf{i}} + 2\hat{\mathbf{j}} \, \text{m} \). What is the work done?

Q4. A force \( \mathbf{F} = 5\hat{\mathbf{i}} + 3\hat{\mathbf{j}} \, \text{N} \) acts on a particle moving along a displacement \( \mathbf{d} = 2\hat{\mathbf{i}} + 4\hat{\mathbf{j}} \, \text{m} \). What is the work done by the force?

Q5. A \( 7 \, \text{kg} \) mass falls from \( 3 \, \text{m} \) onto a spring (\( k = 2000 \, \text{N/m} \)). What is the maximum compression? (Take \( g = 10 \, \text{m/s}^2 \))

Q6. A \( 1000 \, \text{kg} \) car at \( 10 \, \text{m/s} \) hits a spring (\( k = 5 \times 10^3 \, \text{N/m} \)). What is the maximum compression?

Q7. A \( 1 \, \text{kg} \) ball at \( 10 \, \text{m/s} \) collides elastically with a stationary \( 2 \, \text{kg} \) ball. What is the speed of the \( 2 \, \text{kg} \) ball after collision?

Q8. A motor lifts a \( 1700 \, \text{kg} \) load at \( 4 \, \text{m/s} \) against \( 4500 \, \text{N} \) friction. What is the power? (Take \( g = 10 \, \text{m/s}^2 \))

Q9. A spring (\( k = 300 \, \text{N/m} \)) is compressed by \( 0.3 \, \text{m} \). What is the stored potential energy?

Q10. A motor lifts a \( 1800 \, \text{kg} \) load at \( 2.8 \, \text{m/s} \) against \( 3500 \, \text{N} \) friction. What is the power? (Take \( g = 10 \, \text{m/s}^2 \))