NEET Work Energy and Power — Set 2

Question 1

A $ 7 \, \text{kg} $ block is pushed with $ 35 \, \text{N} $ over $ 10 \, \text{m} $ on a frictionless surface, starting from rest. What is its final speed?

Accepted Answer

Work $ W = 35 \times 10 = 350 \, \text{J} $. By work-energy theorem, $ K_f = W \Rightarrow \frac{1}{2} \times 7 \times v^2 = 350 \Rightarrow v^2 = 100 \Rightarrow v = 10 \, \text{m/s} $.

Question 2

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

Question 3

A $ 3.5 \, \text{kg} $ mass falls from $ 7 \, \text{m} $ onto a spring ($ k = 1200 \, \text{N/m} $). What is the maximum compression? (Take $ g = 10 \, \text{m/s}^2 $)

Accepted Answer

Potential energy $ mgh = 3.5 \times 10 \times 7 = 245 \, \text{J} $. Spring energy $ \frac{1}{2} k x_m^2 = 245 \Rightarrow 600 x_m^2 = 245 \Rightarrow x_m = \sqrt{0.4083} \approx 0.639 \, \text{m} $.

NEET Physics: Work Energy and Power — Practice Set 2

Q1. A \( 7 \, \text{kg} \) block is pushed with \( 35 \, \text{N} \) over \( 10 \, \text{m} \) on a frictionless surface, starting from rest. What is its final speed?

Q2. A \( 2 \, \text{kg} \) 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 \( 3.5 \, \text{kg} \) mass falls from \( 7 \, \text{m} \) onto a spring (\( k = 1200 \, \text{N/m} \)). What is the maximum compression? (Take \( g = 10 \, \text{m/s}^2 \))

Q4. A bullet of mass \( 20 \, \text{g} \) with speed \( 300 \, \text{m/s} \) passes through a wooden block and emerges with \( 20\% \) of its initial kinetic energy. What is the emergent speed?

Q5. A \( 2.5 \, \text{kg} \) block slides down a frictionless incline from \( 10 \, \text{m} \) height. What is its speed at the bottom? (Take \( g = 10 \, \text{m/s}^2 \))

Q6. A force \( F = 2x \, \text{N} \) acts on a particle from \( x = 1 \, \text{m} \) to \( x = 3 \, \text{m} \). What is the work done?

Q7. A \( 1.8 \, \text{kg} \) object is dropped from \( 18 \, \text{m} \). What is its kinetic energy just before hitting the ground? (Take \( g = 10 \, \text{m/s}^2 \))

Q8. A \( 5 \, \text{kg} \) block is pushed with \( 25 \, \text{N} \) over \( 8 \, \text{m} \) on a frictionless surface, starting from \( 1 \, \text{m/s} \). What is its final speed?

Q9. A \( 7 \, \text{kg} \) mass at \( 14 \, \text{m/s} \) collides elastically with an identical stationary mass. What is the speed of the first mass after collision?

Q10. A spring (\( k = 900 \, \text{N/m} \)) is compressed from \( 0.15 \, \text{m} \) to \( 0.25 \, \text{m} \). What is the work done by the spring force?

Q11. A spring (\( k = 450 \, \text{N/m} \)) is compressed by \( 0.15 \, \text{m} \). What is the stored potential energy?

Q12. A \( 1200 \, \text{kg} \) car moving at \( 15 \, \text{m/s} \) compresses a spring (\( k = 8 \times 10^3 \, \text{N/m} \)). What is the maximum compression?

Q13. A \( 9 \, \text{kg} \) mass falls from \( 6 \, \text{m} \) onto a spring (\( k = 3000 \, \text{N/m} \)). What is the maximum compression? (Take \( g = 10 \, \text{m/s}^2 \))

Q14. A force \( F = 8x \, \text{N} \) acts from \( x = 0 \) to \( x = 2 \, \text{m} \). What is the work done?

Q15. A force \( \mathbf{F} = 7\hat{\mathbf{i}} - 3\hat{\mathbf{j}} \, \text{N} \) acts on a particle moving along \( \mathbf{d} = 2\hat{\mathbf{i}} + 6\hat{\mathbf{j}} \, \text{m} \). What is the work done?