NEET Work Energy and Power — Set 3

Question 1

A spring ($ k = 600 \, \text{N/m} $) is stretched by $ 0.2 \, \text{m} $. What is the stored potential energy?

Accepted Answer

Potential energy $ V = \frac{1}{2} k x^2 = \frac{1}{2} \times 600 \times (0.2)^2 = 300 \times 0.04 = 12 \, \text{J} $.

Question 2

A neutron ($ 1 \, \text{u} $) at $ 7 \times 10^6 \, \text{m/s} $ collides elastically with a carbon ($ 12 \, \text{u} $). What fraction of its kinetic energy is retained?

Accepted Answer

Fraction retained $ f_1 = \left( \frac{m_1 - m_2}{m_1 + m_2} \right)^2 = \left( \frac{1 - 12}{1 + 12} \right)^2 = \left( \frac{-11}{13} \right)^2 = \frac{121}{169} \approx 0.716 $.

Question 3

A $ 11 \, \text{kg} $ mass at $ 18 \, \text{m/s} $ collides elastically with an identical stationary mass. What is the speed of the first mass after collision?

Accepted Answer

For equal masses in elastic collision, $ v_{1f} = 0 \, \text{m/s} $ (first mass stops).

NEET Physics: Work Energy and Power — Practice Set 3

Q1. A spring (\( k = 600 \, \text{N/m} \)) is stretched by \( 0.2 \, \text{m} \). What is the stored potential energy?

Q2. A neutron (\( 1 \, \text{u} \)) at \( 7 \times 10^6 \, \text{m/s} \) collides elastically with a carbon (\( 12 \, \text{u} \)). What fraction of its kinetic energy is retained?

Q3. A \( 11 \, \text{kg} \) mass at \( 18 \, \text{m/s} \) collides elastically with an identical stationary mass. What is the speed of the first mass after collision?

Q4. A \( 1.2 \, \text{kg} \) object is dropped from \( 15 \, \text{m} \). What is its speed just before hitting the ground? (Take \( g = 10 \, \text{m/s}^2 \))

Q5. A \( 10 \, \text{kg} \) mass at \( 16 \, \text{m/s} \) collides elastically with an identical stationary mass. What is the speed of the second mass after collision?

Q6. A \( 2 \, \text{kg} \) ball moving at \( 6 \, \text{m/s} \) collides elastically with a stationary \( 4 \, \text{kg} \) ball. What is the speed of the \( 4 \, \text{kg} \) ball after collision?

Q7. A force \( \mathbf{F} = 3\hat{\mathbf{i}} - 4\hat{\mathbf{j}} \, \text{N} \) acts on a particle moving along \( \mathbf{d} = 5\hat{\mathbf{i}} + 5\hat{\mathbf{j}} \, \text{m} \). What is the work done?

Q8. A force \( F = 3x^3 \, \text{N} \) acts from \( x = 0 \) to \( x = 2 \, \text{m} \). What is the work done?

Q9. A motor lifts a \( 1500 \, \text{kg} \) elevator at \( 4 \, \text{m/s} \) against \( 2000 \, \text{N} \) friction. What is the power delivered? (Take \( g = 10 \, \text{m/s}^2 \))

Q10. A spring (\( k = 500 \, \text{N/m} \)) is stretched by \( 0.3 \, \text{m} \). What is the stored potential energy?

Q11. A spring (\( k = 1000 \, \text{N/m} \)) is stretched from \( 0.1 \, \text{m} \) to \( 0.2 \, \text{m} \). What is the work done by the spring force?

Q12. A \( 6 \, \text{kg} \) block at \( 11 \, \text{m/s} \) encounters a force \( F = \frac{-1.8}{x} \, \text{N} \) from \( x = 0.9 \, \text{m} \) to \( x = 4.5 \, \text{m} \). What is the final speed?

Q13. A \( 0.8 \, \text{g} \) drop falls from \( 200 \, \text{m} \) and hits the ground at \( 14 \, \text{m/s} \). What is the work done by air resistance? (Take \( g = 10 \, \text{m/s}^2 \))

Q14. A \( 14 \, \text{kg} \) mass is lifted \( 7 \, \text{m} \) in \( 5 \, \text{s} \) at constant speed. What is the power? (Take \( g = 10 \, \text{m/s}^2 \))