NEET Work Energy and Power — Set 15

Question 1

A $ 2.5 \, \text{kg} $ object is dropped from $ 13 \, \text{m} $. What is its kinetic energy just before hitting the ground? (Take $ g = 10 \, \text{m/s}^2 $)

Accepted Answer

Potential energy $ V = mgh = 2.5 \times 10 \times 13 = 325 \, \text{J} $. By conservation, $ K_f = V_i = 325 \, \text{J} $.

Question 2

A $ 6 \, \text{kg} $ mass falls from $ 4 \, \text{m} $ onto a spring ($ k = 1500 \, \text{N/m} $). What is the maximum compression? (Take $ g = 10 \, \text{m/s}^2 $)

Accepted Answer

Potential energy $ mgh = 6 \times 10 \times 4 = 240 \, \text{J} $. Spring energy $ \frac{1}{2} k x_m^2 = 240 \Rightarrow 750 x_m^2 = 240 \Rightarrow x_m = \sqrt{0.32} \approx 0.566 \, \text{m} $.

Question 3

A $ 0.8 \, \text{kg} $ pendulum bob completes a vertical circle of radius $ 2.5 \, \text{m} $. What is the speed at the top? (Take $ g = 10 \, \text{m/s}^2 $)

Accepted Answer

At top, minimum speed $ v_C = \sqrt{gL} = \sqrt{10 \times 2.5} = \sqrt{25} = 5 \, \text{m/s} $.

NEET Physics: Work Energy and Power — Practice Set 15

Q1. A \( 2.5 \, \text{kg} \) object is dropped from \( 13 \, \text{m} \). What is its kinetic energy just before hitting the ground? (Take \( g = 10 \, \text{m/s}^2 \))

Q2. A \( 6 \, \text{kg} \) mass falls from \( 4 \, \text{m} \) onto a spring (\( k = 1500 \, \text{N/m} \)). What is the maximum compression? (Take \( g = 10 \, \text{m/s}^2 \))

Q3. A \( 0.8 \, \text{kg} \) pendulum bob completes a vertical circle of radius \( 2.5 \, \text{m} \). What is the speed at the top? (Take \( g = 10 \, \text{m/s}^2 \))

Q4. A person applies a force of \( 120 \, \text{N} \) over \( 5 \, \text{m} \), then the force decreases linearly to \( 40 \, \text{N} \) over \( 10 \, \text{m} \). What is the total work done?

Q5. A \( 1600 \, \text{kg} \) car at \( 15 \, \text{m/s} \) hits a spring (\( k = 10^4 \, \text{N/m} \)). What is the maximum compression?

Q6. A \( 5 \, \text{kg} \) mass at \( 8 \, \text{m/s} \) collides inelastically with a stationary \( 3 \, \text{kg} \) mass. What is the final speed?

Q7. A \( 0.4 \, \text{kg} \) pendulum bob completes a vertical circle of radius \( 1.8 \, \text{m} \). What is the speed at the bottom? (Take \( g = 10 \, \text{m/s}^2 \))

Q8. A \( 4 \, \text{kg} \) mass moving at \( 5 \, \text{m/s} \) collides inelastically with a stationary \( 6 \, \text{kg} \) mass. What is their common speed after collision?

Q9. A \( 6 \, \text{kg} \) block is pushed with \( 30 \, \text{N} \) over \( 5 \, \text{m} \) on a frictionless surface, starting from rest. What is its final speed?

Q10. A \( 3 \, \text{kg} \) block slides down a frictionless incline from \( 7 \, \text{m} \) height. What is its speed at the bottom? (Take \( g = 10 \, \text{m/s}^2 \))