NEET Work Energy and Power — Set 8

Question 1

A $ 40 \, \text{g} $ bullet at $ 900 \, \text{m/s} $ emerges from a block with $ 60\% $ of its initial kinetic energy. What is its emergent speed?

Accepted Answer

Initial $ K = \frac{1}{2} \times 0.04 \times 900^2 = 16200 \, \text{J} $. Final $ K = 0.6 \times 16200 = 9720 \, \text{J} $. $ \frac{1}{2} \times 0.04 \times v_f^2 = 9720 \Rightarrow v_f^2 = 486000 \Rightarrow v_f = \sqrt{486000} \approx 697.1 \, \text{m/s} $.

Question 2

A $ 1500 \, \text{kg} $ car at $ 20 \, \text{m/s} $ hits a spring ($ k = 9 \times 10^3 \, \text{N/m} $). What is the maximum compression?

Accepted Answer

Initial $ K = \frac{1}{2} \times 1500 \times 20^2 = 300000 \, \text{J} $. Spring energy $ \frac{1}{2} k x_m^2 = 300000 \Rightarrow 4500 x_m^2 = 300000 \Rightarrow x_m = \sqrt{66.67} \approx 8.16 \, \text{m} $.

Question 3

A force starts at $ 60 \, \text{N} $ over $ 5 \, \text{m} $, then decreases linearly to $ 20 \, \text{N} $ over $ 5 \, \text{m} $. What is the total work done?

Accepted Answer

Work in first part: $ W_1 = 60 \times 5 = 300 \, \text{J} $. Work in second part: $ W_2 = \frac{1}{2} (60 + 20) \times 5 = 40 \times 5 = 200 \, \text{J} $. Total work: $ W = 300 + 200 = 500 \, \text{J} $.

NEET Physics: Work Energy and Power — Practice Set 8

Q1. A \( 40 \, \text{g} \) bullet at \( 900 \, \text{m/s} \) emerges from a block with \( 60\% \) of its initial kinetic energy. What is its emergent speed?

Q2. A \( 1500 \, \text{kg} \) car at \( 20 \, \text{m/s} \) hits a spring (\( k = 9 \times 10^3 \, \text{N/m} \)). What is the maximum compression?

Q3. A force starts at \( 60 \, \text{N} \) over \( 5 \, \text{m} \), then decreases linearly to \( 20 \, \text{N} \) over \( 5 \, \text{m} \). What is the total work done?

Q4. A \( 2 \, \text{kg} \) object is dropped from \( 14 \, \text{m} \). What is its speed just before hitting the ground? (Take \( g = 10 \, \text{m/s}^2 \))

Q5. A spring (\( k = 800 \, \text{N/m} \)) is compressed from \( 0.08 \, \text{m} \) to \( 0.12 \, \text{m} \). What is the work done by the spring force?

Q6. A \( 3.5 \, \text{kg} \) block slides down a frictionless incline from \( 8 \, \text{m} \) height. What is its speed at the bottom? (Take \( g = 10 \, \text{m/s}^2 \))

Q7. A \( 1.5 \, \text{kg} \) pendulum bob completes a vertical circle of radius \( 1.8 \, \text{m} \). What is the speed at the bottom? (Take \( g = 10 \, \text{m/s}^2 \))

Q8. A spring (\( k = 400 \, \text{N/m} \)) is stretched by \( 0.25 \, \text{m} \). What is the stored potential energy?

Q9. A cyclist applies a force of \( 150 \, \text{N} \) over \( 8 \, \text{m} \), then the force decreases linearly to \( 50 \, \text{N} \) over the next \( 12 \, \text{m} \). What is the total work done by the cyclist?

Q10. A neutron (\( 1 \, \text{u} \)) at \( 5 \times 10^6 \, \text{m/s} \) collides elastically with a deuterium (\( 2 \, \text{u} \)). What fraction of its kinetic energy is retained?