NEET Work Energy and Power — Set 13

Question 1

A force $ F = 5x \, \text{N} $ acts from $ x = 0 $ to $ x = 3 \, \text{m} $. What is the work done?

Accepted Answer

Work $ W = \int_0^3 5x \, dx = \left[ \frac{5}{2} x^2 \right]_0^3 = \frac{5}{2} \times 9 = 22.5 \, \text{J} $.

Question 2

A block of mass $ 1 \, \text{kg} $ moves on a rough surface with initial speed $ 4 \, \text{m/s} $. A retarding force $ F = \frac{-0.8}{x} \, \text{N} $ acts from $ x = 0.2 \, \text{m} $ to $ x = 2 \, \text{m} $. What is the final speed?

Accepted Answer

Initial $ K = \frac{1}{2} \times 1 \times 4^2 = 8 \, \text{J} $. Work done by force: $ W = \int_{0.2}^{2} \frac{-0.8}{x} \, dx = -0.8 \ln(x) \Big|_{0.2}^{2} = -0.8 (\ln 2 - \ln 0.2) = -0.8 \ln 10 \approx -1.84 \, \text{J} $. Final $ K = 8 - 1.84 = 6.16 \, \text{J} $. $ v_f = \sqrt{\frac{2 \times 6.16}{1}} \approx 3.5 \, \text{m/s} $.

Question 3

A $ 10 \, \text{kg} $ mass at $ 8 \, \text{m/s} $ collides inelastically with a stationary $ 5 \, \text{kg} $ mass. What is the final speed?

Accepted Answer

Momentum conservation: $ 10 \times 8 = (10 + 5) v_f \Rightarrow 80 = 15 v_f \Rightarrow v_f = \frac{80}{15} \approx 5.33 \, \text{m/s} $.

NEET Physics: Work Energy and Power — Practice Set 13

Q1. A force \( F = 5x \, \text{N} \) acts from \( x = 0 \) to \( x = 3 \, \text{m} \). What is the work done?

Q2. A block of mass \( 1 \, \text{kg} \) moves on a rough surface with initial speed \( 4 \, \text{m/s} \). A retarding force \( F = \frac{-0.8}{x} \, \text{N} \) acts from \( x = 0.2 \, \text{m} \) to \( x = 2 \, \text{m} \). What is the final speed?

Q3. A \( 10 \, \text{kg} \) mass at \( 8 \, \text{m/s} \) collides inelastically with a stationary \( 5 \, \text{kg} \) mass. What is the final speed?

Q4. A \( 9 \, \text{kg} \) mass at \( 7 \, \text{m/s} \) collides inelastically with a stationary \( 3 \, \text{kg} \) mass. What is the final speed?

Q5. A spring (\( k = 500 \, \text{N/m} \)) is stretched from \( 0.12 \, \text{m} \) to \( 0.18 \, \text{m} \). What is the work done by the spring force?

Q6. A \( 10 \, \text{kg} \) mass is lifted \( 5 \, \text{m} \) in \( 2 \, \text{s} \) at constant speed. What is the power? (Take \( g = 10 \, \text{m/s}^2 \))

Q7. A force \( F = 6x^2 \, \text{N} \) acts from \( x = 0 \) to \( x = 1 \, \text{m} \). What is the work done?

Q8. A \( 1.5 \, \text{kg} \) ball at \( 15 \, \text{m/s} \) collides elastically with a stationary \( 4.5 \, \text{kg} \) ball. What is the speed of the \( 1.5 \, \text{kg} \) ball after collision?

Q9. A \( 3 \, \text{kg} \) block at \( 8 \, \text{m/s} \) encounters a force \( F = \frac{-1.2}{x} \, \text{N} \) from \( x = 0.5 \, \text{m} \) to \( x = 2.5 \, \text{m} \). What is the final speed?

Q10. A block of mass \( 2 \, \text{kg} \) is pushed with a constant force of \( 10 \, \text{N} \) over a distance of \( 5 \, \text{m} \) on a frictionless surface. What is the final kinetic energy of the block if it starts from rest?