NEET Work Energy and Power — Set 14

Question 1

A motor lifts a $ 1400 \, \text{kg} $ load at $ 3.5 \, \text{m/s} $ against $ 3000 \, \text{N} $ friction. What is the power? (Take $ g = 10 \, \text{m/s}^2 $)

Accepted Answer

Force $ F = mg + F_f = 1400 \times 10 + 3000 = 17000 \, \text{N} $. Power $ P = F \cdot v = 17000 \times 3.5 = 59500 \, \text{W} $.

Question 2

A neutron ($ 1 \, \text{u} $) at $ 5 \times 10^5 \, \text{m/s} $ collides elastically with a deuterium ($ 2 \, \text{u} $). What fraction of its kinetic energy is transferred?

Accepted Answer

Fraction transferred $ f_2 = \frac{4 m_1 m_2}{(m_1 + m_2)^2} = \frac{4 \times 1 \times 2}{(1 + 2)^2} = \frac{8}{9} \approx 0.89 $.

Question 3

A $ 3 \, \text{kg} $ mass falls from $ 4 \, \text{m} $ onto a spring ($ k = 600 \, \text{N/m} $). What is the maximum compression? (Take $ g = 10 \, \text{m/s}^2 $)

Accepted Answer

Potential energy $ mgh = 3 \times 10 \times 4 = 120 \, \text{J} $. Spring energy $ \frac{1}{2} k x_m^2 = 120 \Rightarrow 300 x_m^2 = 120 \Rightarrow x_m = \sqrt{0.4} \approx 0.63 \, \text{m} $.

NEET Physics: Work Energy and Power — Practice Set 14

Q1. A motor lifts a \( 1400 \, \text{kg} \) load at \( 3.5 \, \text{m/s} \) against \( 3000 \, \text{N} \) friction. What is the power? (Take \( g = 10 \, \text{m/s}^2 \))

Q2. A neutron (\( 1 \, \text{u} \)) at \( 5 \times 10^5 \, \text{m/s} \) collides elastically with a deuterium (\( 2 \, \text{u} \)). What fraction of its kinetic energy is transferred?

Q3. A \( 3 \, \text{kg} \) mass falls from \( 4 \, \text{m} \) onto a spring (\( k = 600 \, \text{N/m} \)). What is the maximum compression? (Take \( g = 10 \, \text{m/s}^2 \))

Q4. A \( 2 \, \text{kg} \) ball at \( 12 \, \text{m/s} \) collides elastically with a stationary \( 8 \, \text{kg} \) ball. What is the speed of the \( 8 \, \text{kg} \) ball after collision?

Q5. A spring (\( k = 700 \, \text{N/m} \)) is stretched from \( 0.1 \, \text{m} \) to \( 0.2 \, \text{m} \). What is the work done by the spring force?

Q6. A force \( \mathbf{F} = 3\hat{\mathbf{i}} - 7\hat{\mathbf{j}} \, \text{N} \) acts on a particle moving along \( \mathbf{d} = 4\hat{\mathbf{i}} + 3\hat{\mathbf{j}} \, \text{m} \). What is the work done?

Q7. A \( 0.3 \, \text{g} \) drop falls from \( 500 \, \text{m} \) and hits the ground at \( 15 \, \text{m/s} \). What is the work done by air resistance? (Take \( g = 10 \, \text{m/s}^2 \))

Q8. A \( 1 \, \text{kg} \) pendulum bob completes a vertical circle of radius \( 2.2 \, \text{m} \). What is the speed at the bottom? (Take \( g = 10 \, \text{m/s}^2 \))

Q9. Two equal masses collide elastically, one moving at \( 10 \, \text{m/s} \) and the other at rest. What is the speed of the second mass after collision?

Q10. A spring (\( k = 800 \, \text{N/m} \)) is compressed from \( 0.2 \, \text{m} \) to \( 0.3 \, \text{m} \). What is the work done by the spring force?