NEET Work Energy and Power — Set 7

Question 1

A $ 0.5 \, \text{kg} $ pendulum bob is given a speed at the bottom to complete a $ 1 \, \text{m} $ vertical circle. What is the speed at the bottom? (Take $ g = 10 \, \text{m/s}^2 $)

Accepted Answer

At top, $ v_C = \sqrt{gL} $, energy conservation: $ \frac{1}{2} m v_0^2 = \frac{1}{2} m (gL) + 2mgL $. $ v_0^2 = 5gL = 5 \times 10 \times 1 = 50 \Rightarrow v_0 = \sqrt{50} \approx 7.07 \, \text{m/s} $.

Question 2

A $ 2.5 \, \text{kg} $ ball at $ 16 \, \text{m/s} $ collides elastically with a stationary $ 7.5 \, \text{kg} $ ball. What is the speed of the $ 7.5 \, \text{kg} $ ball after collision?

Accepted Answer

For elastic collision: $ v_{2f} = \frac{2 m_1}{m_1 + m_2} v_{1i} = \frac{2 \times 2.5}{2.5 + 7.5} \times 16 = \frac{5}{10} \times 16 = 8 \, \text{m/s} $.

Question 3

A $ 8 \, \text{kg} $ block is pushed with $ 40 \, \text{N} $ over $ 6 \, \text{m} $ on a frictionless surface, starting from $ 2 \, \text{m/s} $. What is its final speed?

Accepted Answer

Initial $ K_i = \frac{1}{2} \times 8 \times 2^2 = 16 \, \text{J} $. Work $ W = 40 \times 6 = 240 \, \text{J} $. Final $ K_f = K_i + W = 16 + 240 = 256 \, \text{J} \Rightarrow v_f = \sqrt{\frac{2 \times 256}{8}} = \sqrt{64} = 8 \, \text{m/s} $.

NEET Physics: Work Energy and Power — Practice Set 7

Q1. A \( 0.5 \, \text{kg} \) pendulum bob is given a speed at the bottom to complete a \( 1 \, \text{m} \) vertical circle. What is the speed at the bottom? (Take \( g = 10 \, \text{m/s}^2 \))

Q2. A \( 2.5 \, \text{kg} \) ball at \( 16 \, \text{m/s} \) collides elastically with a stationary \( 7.5 \, \text{kg} \) ball. What is the speed of the \( 7.5 \, \text{kg} \) ball after collision?

Q3. A \( 8 \, \text{kg} \) block is pushed with \( 40 \, \text{N} \) over \( 6 \, \text{m} \) on a frictionless surface, starting from \( 2 \, \text{m/s} \). What is its final speed?

Q4. A \( 3 \, \text{kg} \) block is pushed with a force of \( 15 \, \text{N} \) over \( 4 \, \text{m} \) on a frictionless horizontal surface. If it starts with a speed of \( 2 \, \text{m/s} \), what is its final kinetic energy?

Q5. A neutron (\( 1 \, \text{u} \)) at \( 3 \times 10^6 \, \text{m/s} \) collides elastically with a deuterium (\( 2 \, \text{u} \)). What fraction of its kinetic energy is retained?

Q6. A force \( \mathbf{F} = 6\hat{\mathbf{i}} + 8\hat{\mathbf{j}} \, \text{N} \) acts on a particle moving along \( \mathbf{d} = 3\hat{\mathbf{i}} - 2\hat{\mathbf{j}} \, \text{m} \). What is the work done?

Q7. In a completely inelastic collision, a \( 3 \, \text{kg} \) mass moving at \( 6 \, \text{m/s} \) collides with a stationary \( 2 \, \text{kg} \) mass. What is the final velocity?

Q8. A neutron (\( 1 \, \text{u} \)) at \( 8 \times 10^6 \, \text{m/s} \) collides elastically with a carbon (\( 12 \, \text{u} \)). What fraction of its kinetic energy is transferred?

Q9. A force \( F = 15x^2 \, \text{N} \) acts from \( x = 0 \) to \( x = 2 \, \text{m} \). What is the work done?

Q10. A force \( F = 3x^2 \, \text{N} \) acts on a particle from \( x = 0 \) to \( x = 2 \, \text{m} \). What is the work done?