NEET Work Energy and Power — Set 1

Question 1

A $ 8 \, \text{kg} $ mass at $ 5 \, \text{m/s} $ collides inelastically with a stationary $ 4 \, \text{kg} $ mass. What is the final speed?

Accepted Answer

Momentum conservation: $ 8 \times 5 = (8 + 4) v_f \Rightarrow 40 = 12 v_f \Rightarrow v_f = \frac{40}{12} \approx 3.33 \, \text{m/s} $.

Question 2

A $ 4 \, \text{kg} $ mass falls from $ 6 \, \text{m} $ onto a spring ($ k = 800 \, \text{N/m} $). What is the maximum compression? (Take $ g = 10 \, \text{m/s}^2 $)

Accepted Answer

Potential energy $ mgh = 4 \times 10 \times 6 = 240 \, \text{J} $. Spring energy $ \frac{1}{2} k x_m^2 = 240 \Rightarrow 400 x_m^2 = 240 \Rightarrow x_m = \sqrt{0.6} \approx 0.775 \, \text{m} $.

Question 3

A neutron ($ 1 \, \text{u} $) at $ 6 \times 10^6 \, \text{m/s} $ collides elastically with a deuterium ($ 2 \, \text{u} $). What fraction of its kinetic energy is transferred?

Accepted Answer

Fraction transferred $ f_2 = \frac{4 m_1 m_2}{(m_1 + m_2)^2} = \frac{4 \times 1 \times 2}{(1 + 2)^2} = \frac{8}{9} \approx 0.889 $.

NEET Physics: Work Energy and Power — Practice Set 1

Q1. A \( 8 \, \text{kg} \) mass at \( 5 \, \text{m/s} \) collides inelastically with a stationary \( 4 \, \text{kg} \) mass. What is the final speed?

Q2. A \( 4 \, \text{kg} \) mass falls from \( 6 \, \text{m} \) onto a spring (\( k = 800 \, \text{N/m} \)). What is the maximum compression? (Take \( g = 10 \, \text{m/s}^2 \))

Q3. A neutron (\( 1 \, \text{u} \)) at \( 6 \times 10^6 \, \text{m/s} \) collides elastically with a deuterium (\( 2 \, \text{u} \)). What fraction of its kinetic energy is transferred?

Q4. A neutron (\( 1 \, \text{u} \)) moving at \( 10^6 \, \text{m/s} \) collides elastically with a deuterium (\( 2 \, \text{u} \)). What fraction of its kinetic energy is lost?

Q5. A \( 4 \, \text{kg} \) ball at \( 20 \, \text{m/s} \) collides elastically with a stationary \( 12 \, \text{kg} \) ball. What is the speed of the \( 12 \, \text{kg} \) ball after collision?

Q6. A motor lifts a \( 2500 \, \text{kg} \) load at \( 2.5 \, \text{m/s} \) against friction of \( 3000 \, \text{N} \). What is the power output? (Take \( g = 10 \, \text{m/s}^2 \))

Q7. A \( 4 \, \text{kg} \) mass at \( 15 \, \text{m/s} \) collides elastically with an identical stationary mass. What is the speed of the second mass after collision?

Q8. A motor lifts a \( 2000 \, \text{kg} \) elevator at \( 3 \, \text{m/s} \) against a frictional force of \( 5000 \, \text{N} \). What is the power delivered? (Take \( g = 10 \, \text{m/s}^2 \))

Q9. A \( 1400 \, \text{kg} \) car at \( 22 \, \text{m/s} \) hits a spring (\( k = 1.2 \times 10^4 \, \text{N/m} \)). What is the maximum compression?

Q10. A spring (\( k = 600 \, \text{N/m} \)) is stretched from \( 0.15 \, \text{m} \) to \( 0.25 \, \text{m} \). What is the work done by the spring force?

Q11. A \( 6 \, \text{kg} \) mass is lifted \( 5 \, \text{m} \) in \( 2 \, \text{s} \) at constant speed. What is the power? (Take \( g = 10 \, \text{m/s}^2 \))

Q12. A \( 12 \, \text{kg} \) mass at \( 9 \, \text{m/s} \) collides inelastically with a stationary \( 6 \, \text{kg} \) mass. What is the final speed?

Q13. A force \( \mathbf{F} = 6\hat{\mathbf{i}} + 4\hat{\mathbf{j}} \, \text{N} \) acts on a particle moving along \( \mathbf{d} = -2\hat{\mathbf{i}} + 5\hat{\mathbf{j}} \, \text{m} \). What is the work done?

Q14. A \( 35 \, \text{g} \) bullet at \( 1200 \, \text{m/s} \) emerges from a block with \( 80\% \) of its initial kinetic energy. What is its emergent speed?

Q15. A \( 3 \, \text{kg} \) mass moving at \( 12 \, \text{m/s} \) collides elastically with an identical stationary mass. What is the speed of the first mass after collision?