NEET Laws of Motion — Set 18

Question 1

A $ 5.8 \, \text{kg} $ block on a $ 45^\circ $ incline ($ \mu_k = 0.25 $) is pulled upward by a $ 7.8 \, \text{kg} $ mass over a pulley. What is the tension? (Take $ g = 10 \, \text{m/s}^2 $, $ \sin 45^\circ = 0.707 $, $ \cos 45^\circ = 0.707 $)

Accepted Answer

For $ 7.8 \, \text{kg} $: $ 7.8g - T = 7.8a \Rightarrow 78 - T = 7.8a $. For $ 5.8 \, \text{kg} $: $ T - mg \sin 45^\circ - f_k = 5.8a $. $ N = mg \cos 45^\circ = 5.8 \times 10 \times 0.707 = 41.006 \, \text{N} $. Friction: $ f_k = 0.25 \times 41.006 \approx 10.2515 \, \text{N} $. $ mg \sin 45^\circ = 58 \times 0.707 = 41.006 \, \text{N} $. Net force: $ T - 41.006 - 10.2515 = 5.8a \Rightarrow T - 51.2575 = 5.8a $. Solve: $ 78 - T = 7.8a $, $ T - 51.2575 = 5.8a $. Substitute: $ 78 - (5.8a + 51.2575) = 7.8a \Rightarrow 78 - 51.2575 - 5.8a = 7.8a \Rightarrow 26.7425 = 13.6a $. $ a \approx 1.97 \, \text{m/s}^2 $, $ T - 51.2575 = 5.8 \times 1.97 \Rightarrow T - 51.2575 \approx 11.426 \Rightarrow T \approx 62.68 \, \text{N} $.

Question 2

A $ 80 \, \text{kg} $ man in a lift accelerating upward at $ 1.5 \, \text{m/s}^2 $ stands on a scale. What is the reading? (Take $ g = 10 \, \text{m/s}^2 $)

Accepted Answer

Scale reads normal force. Net force: $ N - mg = ma $. $ N - 80 \times 10 = 80 \times 1.5 $. $ N - 800 = 120 \Rightarrow N = 920 \, \text{N} $.

Question 3

Two masses $ 4 \, \text{kg} $ and $ 6 \, \text{kg} $ are connected by a light string over a frictionless pulley. What is the acceleration of the system? (Take $ g = 10 \, \text{m/s}^2 $)

Accepted Answer

For two masses over a pulley, acceleration is $ a = \frac{(m_2 - m_1)g}{m_1 + m_2} $. Here, $ m_2 = 6 \, \text{kg} $ (heavier mass), $ m_1 = 4 \, \text{kg} $, $ g = 10 \, \text{m/s}^2 $. Numerator: $ (m_2 - m_1)g = (6 - 4) \times 10 = 20 $. Denominator: $ m_1 + m_2 = 4 + 6 = 10 $. So, $ a = \frac{20}{10} = 2 \, \text{m/s}^2 $.

NEET Physics: Laws of Motion — Practice Set 18

Q1. A \( 5.8 \, \text{kg} \) block on a \( 45^\circ \) incline (\( \mu_k = 0.25 \)) is pulled upward by a \( 7.8 \, \text{kg} \) mass over a pulley. What is the tension? (Take \( g = 10 \, \text{m/s}^2 \), \( \sin 45^\circ = 0.707 \), \( \cos 45^\circ = 0.707 \))

Q2. A \( 80 \, \text{kg} \) man in a lift accelerating upward at \( 1.5 \, \text{m/s}^2 \) stands on a scale. What is the reading? (Take \( g = 10 \, \text{m/s}^2 \))

Q3. Two masses \( 4 \, \text{kg} \) and \( 6 \, \text{kg} \) are connected by a light string over a frictionless pulley. What is the acceleration of the system? (Take \( g = 10 \, \text{m/s}^2 \))

Q4. A \( 5.2 \, \text{kg} \) block on a \( 53^\circ \) incline (\( \mu_s = 0.3 \)) is pulled upward by a horizontal force just sufficient to start motion. What is the force? (Take \( g = 10 \, \text{m/s}^2 \), \( \sin 53^\circ = 0.8 \), \( \cos 53^\circ = 0.6 \))

Q5. A \( 0.25 \, \text{kg} \) stone is whirled in a horizontal circle of radius \( 2 \, \text{m} \) with a tension of \( 10 \, \text{N} \). What is the speed? (Take \( g = 10 \, \text{m/s}^2 \))

Q6. A \( 0.3 \, \text{kg} \) stone is whirled in a horizontal circle of radius \( 1.6 \, \text{m} \) at \( 45 \, \text{rev/min} \). What is the tension? (Take \( g = 10 \, \text{m/s}^2 \))

Q7. A \( 0.45 \, \text{kg} \) stone in a vertical circle of radius \( 1.8 \, \text{m} \) has a speed of \( 14 \, \text{m/s} \) at the bottom. What is the tension at the top? (Take \( g = 10 \, \text{m/s}^2 \))

Q8. A \( 800 \, \text{kg} \) car turns on a banked road (\( \theta = 20^\circ \)) with radius \( 40 \, \text{m} \) at the optimum speed to avoid friction. What is the speed? (Take \( g = 10 \, \text{m/s}^2 \), \( \tan 20^\circ \approx 0.364 \))

Q9. A \( 0.31 \, \text{kg} \) stone is whirled in a horizontal circle of radius \( 1.3 \, \text{m} \) at \( 54 \, \text{rev/min} \). What is the tension? (Take \( g = 10 \, \text{m/s}^2 \))

Q10. A \( 4 \, \text{kg} \) block on a \( 30^\circ \) incline (\( \mu_s = 0.3 \)) is pushed downward by a horizontal force just sufficient to start motion. What is the force? (Take \( g = 10 \, \text{m/s}^2 \), \( \sin 30^\circ = 0.5 \), \( \cos 30^\circ = 0.866 \))