NEET Work Energy and Power — Set 16

Question 1

A force $ \mathbf{F} = -5\hat{\mathbf{i}} + 2\hat{\mathbf{j}} \, \text{N} $ acts on a particle moving along $ \mathbf{d} = 3\hat{\mathbf{i}} + 4\hat{\mathbf{j}} \, \text{m} $. What is the work done?

Accepted Answer

Work $ W = \mathbf{F} \cdot \mathbf{d} $. $ \mathbf{F} = -5\hat{\mathbf{i}} + 2\hat{\mathbf{j}} $, $ \mathbf{d} = 3\hat{\mathbf{i}} + 4\hat{\mathbf{j}} $. Scalar product: $ W = (-5 \times 3) + (2 \times 4) = -15 + 8 = -7 \, \text{J} $.

Question 2

A $ 0.6 \, \text{g} $ drop falls from $ 300 \, \text{m} $ and hits the ground at $ 18 \, \text{m/s} $. What is the work done by air resistance? (Take $ g = 10 \, \text{m/s}^2 $)

Accepted Answer

Work by gravity $ W_g = mgh = 0.0006 \times 10 \times 300 = 1.8 \, \text{J} $. Final $ K = \frac{1}{2} \times 0.0006 \times 18^2 = 0.0972 \, \text{J} $. $ K_f = W_g + W_r \Rightarrow 0.0972 = 1.8 + W_r \Rightarrow W_r = -1.7028 \, \text{J} \approx -1.7 \, \text{J} $.

Question 3

A $ 8 \, \text{kg} $ mass at $ 12 \, \text{m/s} $ collides elastically with an identical stationary mass. What is the speed of the second mass after collision?

Accepted Answer

For equal masses in elastic collision, $ v_{2f} = v_{1i} = 12 \, \text{m/s} $.

NEET Physics: Work Energy and Power — Practice Set 16

Q1. A force \( \mathbf{F} = -5\hat{\mathbf{i}} + 2\hat{\mathbf{j}} \, \text{N} \) acts on a particle moving along \( \mathbf{d} = 3\hat{\mathbf{i}} + 4\hat{\mathbf{j}} \, \text{m} \). What is the work done?

Q2. A \( 0.6 \, \text{g} \) drop falls from \( 300 \, \text{m} \) and hits the ground at \( 18 \, \text{m/s} \). What is the work done by air resistance? (Take \( g = 10 \, \text{m/s}^2 \))

Q3. A \( 8 \, \text{kg} \) mass at \( 12 \, \text{m/s} \) collides elastically with an identical stationary mass. What is the speed of the second mass after collision?

Q4. A \( 5 \, \text{kg} \) mass falls from \( 5 \, \text{m} \) onto a spring (\( k = 1000 \, \text{N/m} \)). What is the maximum compression? (Take \( g = 10 \, \text{m/s}^2 \))

Q5. A \( 5 \, \text{kg} \) ball at \( 24 \, \text{m/s} \) collides elastically with a stationary \( 15 \, \text{kg} \) ball. What is the speed of the \( 5 \, \text{kg} \) ball after collision?

Q6. A \( 6 \, \text{kg} \) mass at \( 10 \, \text{m/s} \) collides elastically with an identical stationary mass. What is the speed of the second mass after collision?

Q7. A \( 0.6 \, \text{kg} \) pendulum bob completes a vertical circle of radius \( 1.2 \, \text{m} \). What is the speed at the top? (Take \( g = 10 \, \text{m/s}^2 \))

Q8. A neutron (\( 1 \, \text{u} \)) at \( 10^6 \, \text{m/s} \) collides elastically with a carbon (\( 12 \, \text{u} \)). What fraction of its kinetic energy is transferred?

Q9. A \( 5 \, \text{kg} \) mass is lifted \( 10 \, \text{m} \) at constant speed by a motor. What is the power if it takes \( 4 \, \text{s} \)? (Take \( g = 10 \, \text{m/s}^2 \))

Q10. A \( 5 \, \text{kg} \) block slides down a frictionless incline from \( 6 \, \text{m} \) height. What is its speed at the bottom? (Take \( g = 10 \, \text{m/s}^2 \))