NEET Work Energy and Power — Set 9

Question 1

A $ 0.7 \, \text{g} $ drop falls from $ 250 \, \text{m} $ and hits the ground at $ 16 \, \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 = 0.0007 \times 10 \times 250 = 1.75 \, \text{J} $. Final $ K = \frac{1}{2} \times 0.0007 \times 16^2 = 0.0896 \, \text{J} $. $ K_f = W_g + W_r \Rightarrow 0.0896 = 1.75 + W_r \Rightarrow W_r = -1.6604 \, \text{J} \approx -1.66 \, \text{J} $.

Question 2

A $ 0.4 \, \text{g} $ drop falls from $ 400 \, \text{m} $ and hits the ground at $ 25 \, \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 = 0.0004 \times 10 \times 400 = 1.6 \, \text{J} $. Final $ K = \frac{1}{2} \times 0.0004 \times 25^2 = 0.125 \, \text{J} $. $ K_f = W_g + W_r \Rightarrow 0.125 = 1.6 + W_r \Rightarrow W_r = -1.475 \, \text{J} $.

Question 3

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

Accepted Answer

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

NEET Physics: Work Energy and Power — Practice Set 9

Q1. A \( 0.7 \, \text{g} \) drop falls from \( 250 \, \text{m} \) and hits the ground at \( 16 \, \text{m/s} \). What is the work done by air resistance? (Take \( g = 10 \, \text{m/s}^2 \))

Q2. A \( 0.4 \, \text{g} \) drop falls from \( 400 \, \text{m} \) and hits the ground at \( 25 \, \text{m/s} \). What is the work done by air resistance? (Take \( g = 10 \, \text{m/s}^2 \))

Q3. A force \( \mathbf{F} = 2\hat{\mathbf{i}} + 5\hat{\mathbf{j}} \, \text{N} \) acts on a particle moving along \( \mathbf{d} = 4\hat{\mathbf{i}} - 3\hat{\mathbf{j}} \, \text{m} \). What is the work done?

Q4. A car of mass \( 1500 \, \text{kg} \) moving at \( 20 \, \text{m/s} \) collides with a spring of constant \( 10^4 \, \text{N/m} \). What is the maximum compression?

Q5. A raindrop of mass \( 2 \, \text{g} \) falls from a height of \( 1 \, \text{km} \) and hits the ground with a speed of \( 40 \, \text{m/s} \). What is the work done by the resistive force? (Take \( g = 10 \, \text{m/s}^2 \))

Q6. A \( 9 \, \text{kg} \) mass is lifted \( 3 \, \text{m} \) in \( 1.5 \, \text{s} \) at constant speed. What is the power? (Take \( g = 10 \, \text{m/s}^2 \))

Q7. A \( 4 \, \text{kg} \) block at \( 9 \, \text{m/s} \) encounters a force \( F = \frac{-1.5}{x} \, \text{N} \) from \( x = 0.6 \, \text{m} \) to \( x = 3 \, \text{m} \). What is the final speed?

Q8. A \( 12 \, \text{kg} \) mass is lifted \( 4 \, \text{m} \) in \( 3 \, \text{s} \) at constant speed. What is the power? (Take \( g = 10 \, \text{m/s}^2 \))

Q9. A \( 800 \, \text{kg} \) car at \( 12 \, \text{m/s} \) hits a spring (\( k = 4 \times 10^3 \, \text{N/m} \)). What is the maximum compression?

Q10. A force starts at \( 75 \, \text{N} \) over \( 3 \, \text{m} \), then decreases linearly to \( 15 \, \text{N} \) over \( 6 \, \text{m} \). What is the total work done?