NEET Work Energy and Power — Set 12

Question 1

A $ 8 \, \text{kg} $ block at $ 14 \, \text{m/s} $ encounters a force $ F = \frac{-3}{x} \, \text{N} $ from $ x = 1.2 \, \text{m} $ to $ x = 6 \, \text{m} $. What is the final speed?

Accepted Answer

Initial $ K = \frac{1}{2} \times 8 \times 14^2 = 784 \, \text{J} $. Work $ W = \int_{1.2}^{6} \frac{-3}{x} \, dx = -3 \ln(6/1.2) = -3 \ln 5 \approx -4.83 \, \text{J} $. Final $ K = 784 - 4.83 = 779.17 \, \text{J} \Rightarrow v_f = \sqrt{\frac{2 \times 779.17}{8}} \approx 13.94 \, \text{m/s} $.

Question 2

A $ 5 \, \text{kg} $ block slides down a frictionless incline from $ 9 \, \text{m} $ height. What is its speed at the bottom? (Take $ g = 10 \, \text{m/s}^2 $)

Accepted Answer

Potential energy $ mgh = 5 \times 10 \times 9 = 450 \, \text{J} $. Kinetic energy $ \frac{1}{2} m v^2 = 450 \Rightarrow v^2 = 180 \Rightarrow v = \sqrt{180} \approx 13.42 \, \text{m/s} $.

Question 3

A $ 2.5 \, \text{kg} $ block at $ 7 \, \text{m/s} $ encounters a force $ F = \frac{-0.9}{x} \, \text{N} $ from $ x = 0.4 \, \text{m} $ to $ x = 2 \, \text{m} $. What is the final speed?

Accepted Answer

Initial $ K = \frac{1}{2} \times 2.5 \times 7^2 = 61.25 \, \text{J} $. Work $ W = \int_{0.4}^{2} \frac{-0.9}{x} \, dx = -0.9 \ln(2/0.4) = -0.9 \ln 5 \approx -1.45 \, \text{J} $. Final $ K = 61.25 - 1.45 = 59.8 \, \text{J} \Rightarrow v_f = \sqrt{\frac{2 \times 59.8}{2.5}} \approx 6.92 \, \text{m/s} $.

NEET Physics: Work Energy and Power — Practice Set 12

Q1. A \( 8 \, \text{kg} \) block at \( 14 \, \text{m/s} \) encounters a force \( F = \frac{-3}{x} \, \text{N} \) from \( x = 1.2 \, \text{m} \) to \( x = 6 \, \text{m} \). What is the final speed?

Q2. A \( 5 \, \text{kg} \) block slides down a frictionless incline from \( 9 \, \text{m} \) height. What is its speed at the bottom? (Take \( g = 10 \, \text{m/s}^2 \))

Q3. A \( 2.5 \, \text{kg} \) block at \( 7 \, \text{m/s} \) encounters a force \( F = \frac{-0.9}{x} \, \text{N} \) from \( x = 0.4 \, \text{m} \) to \( x = 2 \, \text{m} \). What is the final speed?

Q4. A neutron (\( 1 \, \text{u} \)) at \( 4 \times 10^6 \, \text{m/s} \) collides elastically with a carbon (\( 12 \, \text{u} \)). What fraction of its kinetic energy is retained?

Q5. A \( 15 \, \text{g} \) bullet at \( 800 \, \text{m/s} \) emerges from a target with \( 25\% \) of its initial kinetic energy. What is its emergent speed?

Q6. A \( 11 \, \text{kg} \) mass at \( 6 \, \text{m/s} \) collides inelastically with a stationary \( 4 \, \text{kg} \) mass. What is the final speed?

Q7. A \( 1.5 \, \text{kg} \) block slides down a frictionless incline from \( 12 \, \text{m} \) height. What is its speed at the bottom? (Take \( g = 10 \, \text{m/s}^2 \))

Q8. A \( 9 \, \text{kg} \) mass at \( 15 \, \text{m/s} \) collides elastically with an identical stationary mass. What is the speed of the first mass after collision?

Q9. A \( 2.5 \, \text{kg} \) mass falls from \( 8 \, \text{m} \) onto a spring (\( k = 1000 \, \text{N/m} \)). What is the maximum compression? (Take \( g = 10 \, \text{m/s}^2 \))

Q10. A pendulum bob of mass \( 2 \, \text{kg} \) is given a horizontal velocity \( v_0 \) at the bottom to just complete a vertical circle of radius \( 1.5 \, \text{m} \). What is \( v_0 \)? (Take \( g = 10 \, \text{m/s}^2 \))