NEET Laws of Motion — Set 15

Question 1

A $ 10 \, \text{kg} $ block on a horizontal surface ($ \mu_k = 0.2 $) is pulled by a $ 6 \, \text{kg} $ mass over a pulley. A $ 20 \, \text{N} $ force opposes the $ 10 \, \text{kg} $ block. What is the acceleration? (Take $ g = 10 \, \text{m/s}^2 $)

Accepted Answer

For $ 6 \, \text{kg} $: $ 6g - T = 6a \Rightarrow 60 - T = 6a $. For $ 10 \, \text{kg} $: $ T - f_k - 20 = 10a $. Normal: $ N = mg = 10 \times 10 = 100 \, \text{N} $. Friction: $ f_k = 0.2 \times 100 = 20 \, \text{N} $. Net force: $ T - 20 - 20 = 10a \Rightarrow T - 40 = 10a $. Solve: $ 60 - T = 6a $, $ T - 40 = 10a $. Substitute: $ 60 - (10a + 40) = 6a \Rightarrow 60 - 40 - 10a = 6a \Rightarrow 20 = 16a $. $ a = \frac{20}{16} = 1.25 \, \text{m/s}^2 $.

Question 2

A $ 7 \, \text{kg} $ block on a horizontal surface ($ \mu_k = 0.3 $) is pulled by a $ 4 \, \text{kg} $ mass over a pulley. A $ 14 \, \text{N} $ force opposes the $ 7 \, \text{kg} $ block. What is the acceleration? (Take $ g = 10 \, \text{m/s}^2 $)

Accepted Answer

For $ 4 \, \text{kg} $: $ 4g - T = 4a \Rightarrow 40 - T = 4a $. For $ 7 \, \text{kg} $: $ T - f_k - 14 = 7a $. Normal: $ N = mg = 7 \times 10 = 70 \, \text{N} $. Friction: $ f_k = 0.3 \times 70 = 21 \, \text{N} $. Net force: $ T - 21 - 14 = 7a \Rightarrow T - 35 = 7a $. Solve: $ 40 - T = 4a $, $ T - 35 = 7a $. Substitute: $ 40 - (7a + 35) = 4a \Rightarrow 40 - 35 - 7a = 4a \Rightarrow 5 = 11a $. $ a = \frac{5}{11} \approx 0.45 \, \text{m/s}^2 $.

Question 3

A $ 1350 \, \text{kg} $ car turns on a banked road ($ \theta = 25^\circ $) with radius $ 50 \, \text{m} $ at the optimum speed to avoid friction. What is the speed? (Take $ g = 10 \, \text{m/s}^2 $, $ \tan 25^\circ \approx 0.466 $)

Accepted Answer

Optimum speed: $ v_0 = \sqrt{rg \tan\theta} $ (no friction contribution). Substitute: $ r = 50 \, \text{m} $, $ g = 10 \, \text{m/s}^2 $, $ \tan 25^\circ = 0.466 $. $ v_0^2 = 50 \times 10 \times 0.466 = 500 \times 0.466 = 233 $. $ v_0 = \sqrt{233} \approx 15.26 \, \text{m/s} $.

NEET Physics: Laws of Motion — Practice Set 15

Q1. A \( 10 \, \text{kg} \) block on a horizontal surface (\( \mu_k = 0.2 \)) is pulled by a \( 6 \, \text{kg} \) mass over a pulley. A \( 20 \, \text{N} \) force opposes the \( 10 \, \text{kg} \) block. What is the acceleration? (Take \( g = 10 \, \text{m/s}^2 \))

Q2. A \( 7 \, \text{kg} \) block on a horizontal surface (\( \mu_k = 0.3 \)) is pulled by a \( 4 \, \text{kg} \) mass over a pulley. A \( 14 \, \text{N} \) force opposes the \( 7 \, \text{kg} \) block. What is the acceleration? (Take \( g = 10 \, \text{m/s}^2 \))

Q3. A \( 1350 \, \text{kg} \) car turns on a banked road (\( \theta = 25^\circ \)) with radius \( 50 \, \text{m} \) at the optimum speed to avoid friction. What is the speed? (Take \( g = 10 \, \text{m/s}^2 \), \( \tan 25^\circ \approx 0.466 \))

Q4. A \( 0.26 \, \text{kg} \) ball moving at \( 22 \, \text{m/s} \) at \( 60^\circ \) to a wall rebounds at the same speed and angle. What is the impulse perpendicular to the wall? (Take \( \sin 60^\circ = 0.866 \), \( \cos 60^\circ = 0.5 \))

Q5. A \( 9 \, \text{kg} \) block on a horizontal surface (\( \mu_k = 0.25 \)) is pulled by a \( 5 \, \text{kg} \) mass over a pulley. A \( 15 \, \text{N} \) force aids the \( 9 \, \text{kg} \) block. What is the tension? (Take \( g = 10 \, \text{m/s}^2 \))

Q6. A \( 2000 \, \text{kg} \) rocket accelerates upward at \( 6 \, \text{m/s}^2 \) while ejecting gas at \( 100 \, \text{kg/s} \) with speed \( 50 \, \text{m/s} \) relative to the rocket. What is the thrust? (Take \( g = 10 \, \text{m/s}^2 \))

Q7. A \( 0.22 \, \text{kg} \) ball moving at \( 16 \, \text{m/s} \) strikes a wall perpendicularly and rebounds at \( 12 \, \text{m/s} \). What is the impulse? (Take \( g = 10 \, \text{m/s}^2 \))

Q8. A \( 3.8 \, \text{kg} \) block on a horizontal surface (\( \mu_k = 0.25 \)) is connected to a \( 5.8 \, \text{kg} \) mass over a pulley. A \( 14 \, \text{N} \) force opposes the \( 3.8 \, \text{kg} \) block. What is the acceleration? (Take \( g = 10 \, \text{m/s}^2 \))

Q9. A \( 6 \, \text{kg} \) block on a \( 37^\circ \) incline (\( \mu_s = 0.35 \)) is pulled downward by a horizontal force just sufficient to start motion. What is the force? (Take \( g = 10 \, \text{m/s}^2 \), \( \sin 37^\circ = 0.6 \), \( \cos 37^\circ = 0.8 \))

Q10. A \( 5 \, \text{kg} \) block on a horizontal surface (\( \mu_k = 0.2 \)) is pulled by a \( 20 \, \text{N} \) force via a pulley with a hanging \( 2 \, \text{kg} \) mass. What is the system’s acceleration? (Take \( g = 10 \, \text{m/s}^2 \))