NEET Laws of Motion — Set 3

Question 1

A $ 6.2 \, \text{kg} $ block on a horizontal surface ($ \mu_k = 0.2 $) is pulled by a $ 4.2 \, \text{kg} $ mass over a pulley. A $ 13 \, \text{N} $ force aids the $ 6.2 \, \text{kg} $ block. What is the tension? (Take $ g = 10 \, \text{m/s}^2 $)

Accepted Answer

For $ 4.2 \, \text{kg} $: $ 4.2g - T = 4.2a \Rightarrow 42 - T = 4.2a $. For $ 6.2 \, \text{kg} $: $ T + 13 - f_k = 6.2a $. Normal: $ N = mg = 6.2 \times 10 = 62 \, \text{N} $. Friction: $ f_k = 0.2 \times 62 = 12.4 \, \text{N} $. Net force: $ T + 13 - 12.4 = 6.2a \Rightarrow T + 0.6 = 6.2a $. Solve: $ 42 - T = 4.2a $, $ T + 0.6 = 6.2a $. Substitute: $ 42 - (6.2a - 0.6) = 4.2a \Rightarrow 42 + 0.6 - 6.2a = 4.2a \Rightarrow 42.6 = 10.4a $. $ a \approx 4.1 \, \text{m/s}^2 $, $ T + 0.6 = 6.2 \times 4.1 \Rightarrow T + 0.6 \approx 25.42 \Rightarrow T \approx 24.82 \, \text{N} $.

Question 2

A $ 50 \, \text{kg} $ man in a lift descending at $ 5 \, \text{m/s}^2 $ pushes a $ 10 \, \text{kg} $ box downward with $ 20 \, \text{N} $. What is the normal force on the floor? (Take $ g = 10 \, \text{m/s}^2 $)

Accepted Answer

For box: $ N_b - mg - F = ma \Rightarrow N_b - 10 \times 10 - 20 = 10 \times (-5) $. $ N_b - 100 - 20 = -50 \Rightarrow N_b - 120 = -50 \Rightarrow N_b = 70 \, \text{N} $. For man: $ N_m - mg - N_b = ma \Rightarrow N_m - 50 \times 10 - 70 = 50 \times (-5) $. $ N_m - 500 - 70 = -250 \Rightarrow N_m - 570 = -250 \Rightarrow N_m = 320 \, \text{N} $. Total $ N = N_m + N_b = 320 + 70 = 390 \, \text{N} $.

Question 3

A stone of mass $ 0.2 \, \text{kg} $ is dropped from a height. What is the net force acting on it during its downward motion? (Take $ g = 10 \, \text{m/s}^2 $, ignore air resistance)

Accepted Answer

The stone is in free fall, and the only force acting on it is gravity. The weight of the stone is $ F = mg $. Substitute: $ m = 0.2 \, \text{kg} $, $ g = 10 \, \text{m/s}^2 $. So, $ F = 0.2 \times 10 = 2 \, \text{N} $, directed downward. Since air resistance is ignored, this is the net force.

NEET Physics: Laws of Motion — Practice Set 3

Q1. A \( 6.2 \, \text{kg} \) block on a horizontal surface (\( \mu_k = 0.2 \)) is pulled by a \( 4.2 \, \text{kg} \) mass over a pulley. A \( 13 \, \text{N} \) force aids the \( 6.2 \, \text{kg} \) block. What is the tension? (Take \( g = 10 \, \text{m/s}^2 \))

Q2. A \( 50 \, \text{kg} \) man in a lift descending at \( 5 \, \text{m/s}^2 \) pushes a \( 10 \, \text{kg} \) box downward with \( 20 \, \text{N} \). What is the normal force on the floor? (Take \( g = 10 \, \text{m/s}^2 \))

Q3. A stone of mass \( 0.2 \, \text{kg} \) is dropped from a height. What is the net force acting on it during its downward motion? (Take \( g = 10 \, \text{m/s}^2 \), ignore air resistance)

Q5. A car of mass \( 1200 \, \text{kg} \) takes a turn of radius \( 50 \, \text{m} \) on a banked road at \( 15^\circ \). What is the optimum speed to avoid friction? (Take \( g = 10 \, \text{m/s}^2 \), \( \tan 15^\circ \approx 0.268 \))

Q6. A \( 65 \, \text{kg} \) man in a lift accelerating upward at \( 2.5 \, \text{m/s}^2 \) stands on a scale. What is the reading? (Take \( g = 10 \, \text{m/s}^2 \))

Q7. A \( 70 \, \text{kg} \) man in a lift accelerating downward at \( 3 \, \text{m/s}^2 \) pushes a \( 15 \, \text{kg} \) box upward with \( 50 \, \text{N} \). What is the normal force on the floor? (Take \( g = 10 \, \text{m/s}^2 \))

Q10. A \( 0.34 \, \text{kg} \) stone is whirled in a horizontal circle of radius \( 1.8 \, \text{m} \) at \( 42 \, \text{rev/min} \). What is the tension? (Take \( g = 10 \, \text{m/s}^2 \))