NEET Work Energy and Power — Set 10

Question 1

A $ 20 \, \text{g} $ bullet at $ 1000 \, \text{m/s} $ emerges from a block with $ 70\% $ of its initial kinetic energy. What is its emergent speed?

Accepted Answer

Initial $ K = \frac{1}{2} \times 0.02 \times 1000^2 = 10000 \, \text{J} $. Final $ K = 0.7 \times 10000 = 7000 \, \text{J} $. $ \frac{1}{2} \times 0.02 \times v_f^2 = 7000 \Rightarrow v_f^2 = 700000 \Rightarrow v_f = \sqrt{700000} \approx 836.7 \, \text{m/s} $.

Question 2

A spring ($ k = 250 \, \text{N/m} $) is compressed by $ 0.4 \, \text{m} $. What is the stored potential energy?

Accepted Answer

Potential energy $ V = \frac{1}{2} k x^2 = \frac{1}{2} \times 250 \times (0.4)^2 = 125 \times 0.16 = 20 \, \text{J} $.

Question 3

A force starts at $ 90 \, \text{N} $ over $ 3 \, \text{m} $, then decreases linearly to $ 40 \, \text{N} $ over $ 7 \, \text{m} $. What is the total work done?

Accepted Answer

Work in first part: $ W_1 = 90 \times 3 = 270 \, \text{J} $. Work in second part: $ W_2 = \frac{1}{2} (90 + 40) \times 7 = 65 \times 7 = 455 \, \text{J} $. Total work: $ W = 270 + 455 = 725 \, \text{J} $.

NEET Physics: Work Energy and Power — Practice Set 10

Q1. A \( 20 \, \text{g} \) bullet at \( 1000 \, \text{m/s} \) emerges from a block with \( 70\% \) of its initial kinetic energy. What is its emergent speed?

Q2. A spring (\( k = 250 \, \text{N/m} \)) is compressed by \( 0.4 \, \text{m} \). What is the stored potential energy?

Q3. A force starts at \( 90 \, \text{N} \) over \( 3 \, \text{m} \), then decreases linearly to \( 40 \, \text{N} \) over \( 7 \, \text{m} \). What is the total work done?

Q4. A \( 2 \, \text{kg} \) block falls from \( 5 \, \text{m} \) onto a spring (\( k = 500 \, \text{N/m} \)). What is the maximum compression? (Take \( g = 10 \, \text{m/s}^2 \))

Q5. A \( 1.2 \, \text{kg} \) pendulum bob completes a vertical circle of radius \( 1.6 \, \text{m} \). What is the speed at the top? (Take \( g = 10 \, \text{m/s}^2 \))

Q6. A \( 25 \, \text{g} \) bullet at \( 600 \, \text{m/s} \) emerges from a target with \( 50\% \) of its initial kinetic energy. What is its emergent speed?

Q7. A ball of mass \( 0.5 \, \text{kg} \) is dropped from a height of \( 8 \, \text{m} \). What is its kinetic energy just before hitting the ground? (Take \( g = 10 \, \text{m/s}^2 \))

Q8. A spring (\( k = 400 \, \text{N/m} \)) is compressed from \( 0.2 \, \text{m} \) to \( 0.35 \, \text{m} \). What is the work done by the spring force?

Q9. A \( 1100 \, \text{kg} \) car at \( 16 \, \text{m/s} \) hits a spring (\( k = 7 \times 10^3 \, \text{N/m} \)). What is the maximum compression?

Q10. A \( 7 \, \text{kg} \) block at \( 12 \, \text{m/s} \) encounters a force \( F = \frac{-2.4}{x} \, \text{N} \) from \( x = 1 \, \text{m} \) to \( x = 5 \, \text{m} \). What is the final speed?