NEET Work Energy and Power — Set 4

Question 1

A $ 10 \, \text{g} $ bullet moving at $ 500 \, \text{m/s} $ emerges from a block with $ 36\% $ of its initial kinetic energy. What is its final speed?

Accepted Answer

Initial $ K = \frac{1}{2} \times 0.01 \times 500^2 = 1250 \, \text{J} $. Final $ K = 0.36 \times 1250 = 450 \, \text{J} $. $ \frac{1}{2} \times 0.01 \times v_f^2 = 450 \Rightarrow v_f^2 = 90000 \Rightarrow v_f = 300 \, \text{m/s} $.

Question 2

A $ 30 \, \text{g} $ bullet at $ 700 \, \text{m/s} $ emerges from a block with $ 40\% $ of its initial kinetic energy. What is its emergent speed?

Accepted Answer

Initial $ K = \frac{1}{2} \times 0.03 \times 700^2 = 7350 \, \text{J} $. Final $ K = 0.4 \times 7350 = 2940 \, \text{J} $. $ \frac{1}{2} \times 0.03 \times v_f^2 = 2940 \Rightarrow v_f^2 = 196000 \Rightarrow v_f = \sqrt{196000} \approx 442.7 \, \text{m/s} $.

Question 3

A $ 1.5 \, \text{kg} $ block at $ 6 \, \text{m/s} $ encounters a force $ F = \frac{-0.6}{x} \, \text{N} $ from $ x = 0.3 \, \text{m} $ to $ x = 1.5 \, \text{m} $. What is the final speed?

Accepted Answer

Initial $ K = \frac{1}{2} \times 1.5 \times 6^2 = 27 \, \text{J} $. Work $ W = \int_{0.3}^{1.5} \frac{-0.6}{x} \, dx = -0.6 \ln(x) \Big|_{0.3}^{1.5} = -0.6 \ln(1.5/0.3) = -0.6 \ln 5 \approx -0.97 \, \text{J} $. Final $ K = 27 - 0.97 = 26.03 \, \text{J} \Rightarrow v_f = \sqrt{\frac{2 \times 26.03}{1.5}} \approx 5.89 \, \text{m/s} $.

NEET Physics: Work Energy and Power — Practice Set 4

Q1. A \( 10 \, \text{g} \) bullet moving at \( 500 \, \text{m/s} \) emerges from a block with \( 36\% \) of its initial kinetic energy. What is its final speed?

Q2. A \( 30 \, \text{g} \) bullet at \( 700 \, \text{m/s} \) emerges from a block with \( 40\% \) of its initial kinetic energy. What is its emergent speed?

Q3. A \( 1.5 \, \text{kg} \) block at \( 6 \, \text{m/s} \) encounters a force \( F = \frac{-0.6}{x} \, \text{N} \) from \( x = 0.3 \, \text{m} \) to \( x = 1.5 \, \text{m} \). What is the final speed?

Q4. A particle moves under a force \( \mathbf{F} = 4\hat{\mathbf{i}} - 2\hat{\mathbf{j}} \, \text{N} \) along a displacement \( \mathbf{d} = 3\hat{\mathbf{i}} + 6\hat{\mathbf{j}} \, \text{m} \). What is the work done by the force?

Q5. A \( 5 \, \text{kg} \) block at \( 10 \, \text{m/s} \) encounters a force \( F = \frac{-2}{x} \, \text{N} \) from \( x = 0.8 \, \text{m} \) to \( x = 4 \, \text{m} \). What is the final speed?

Q6. A \( 1 \, \text{kg} \) ball moving at \( 8 \, \text{m/s} \) undergoes an elastic collision with a stationary \( 3 \, \text{kg} \) ball. What is the speed of the \( 1 \, \text{kg} \) ball after collision?

Q7. A \( 3 \, \text{kg} \) ball at \( 9 \, \text{m/s} \) collides elastically with a stationary \( 6 \, \text{kg} \) ball. What is the speed of the \( 3 \, \text{kg} \) ball after collision?

Q8. A \( 6 \, \text{kg} \) mass at \( 4 \, \text{m/s} \) collides inelastically with a stationary \( 2 \, \text{kg} \) mass. What is the final speed?

Q9. A pendulum bob of \( 1 \, \text{kg} \) completes a vertical circle of radius \( 2 \, \text{m} \) with minimum speed at the bottom. What is the speed at the top? (Take \( g = 10 \, \text{m/s}^2 \))

Q10. A \( 7 \, \text{kg} \) mass at \( 6 \, \text{m/s} \) collides inelastically with a stationary \( 5 \, \text{kg} \) mass. What is the final speed?