NEET Laws of Motion — Set 4

Question 1

A $ 70 \, \text{kg} $ man in a lift accelerating downward at $ 1.2 \, \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 $, where $ a = -1.2 \, \text{m/s}^2 $. $ N - 70 \times 10 = 70 \times (-1.2) $. $ N - 700 = -84 \Rightarrow N = 616 \, \text{N} $.

Question 2

A particle of mass $ 1 \, \text{kg} $ moves with a velocity described by $ y = 2t + 5t^2 $. What is the force acting on it at $ t = 2 \, \text{s} $? (Take $ g = 10 \, \text{m/s}^2 $)

Accepted Answer

Position $ y = 2t + 5t^2 $. Velocity $ v = \frac{dy}{dt} = 2 + 10t $. Acceleration $ a = \frac{dv}{dt} = 10 \, \text{m/s}^2 $. Force $ F = ma = 1 \times 10 = 10 \, \text{N} $ (constant, matches gravity example in PDF). At $ t = 2 \, \text{s} $, $ F = 10 \, \text{N} $.

Question 3

A $ 8 \, \text{kg} $ mass and a $ 12 \, \text{kg} $ mass are connected over a pulley. A $ 20 \, \text{N} $ force pulls the $ 8 \, \text{kg} $ mass upward. What is the acceleration? (Take $ g = 10 \, \text{m/s}^2 $)

Accepted Answer

For $ 12 \, \text{kg} $: $ 12g - T = 12a \Rightarrow 120 - T = 12a $. For $ 8 \, \text{kg} $: $ T + 20 - 8g = 8a \Rightarrow T + 20 - 80 = 8a \Rightarrow T - 60 = 8a $. Solve: $ 120 - T = 12a $, $ T - 60 = 8a $. $ 120 - (8a + 60) = 12a \Rightarrow 120 - 60 - 8a = 12a \Rightarrow 60 = 20a $. $ a = \frac{60}{20} = 3 \, \text{m/s}^2 $.

NEET Physics: Laws of Motion — Practice Set 4

Q1. A \( 70 \, \text{kg} \) man in a lift accelerating downward at \( 1.2 \, \text{m/s}^2 \) stands on a scale. What is the reading? (Take \( g = 10 \, \text{m/s}^2 \))

Q2. A particle of mass \( 1 \, \text{kg} \) moves with a velocity described by \( y = 2t + 5t^2 \). What is the force acting on it at \( t = 2 \, \text{s} \)? (Take \( g = 10 \, \text{m/s}^2 \))

Q3. A \( 8 \, \text{kg} \) mass and a \( 12 \, \text{kg} \) mass are connected over a pulley. A \( 20 \, \text{N} \) force pulls the \( 8 \, \text{kg} \) mass upward. What is the acceleration? (Take \( g = 10 \, \text{m/s}^2 \))

Q4. A \( 0.8 \, \text{kg} \) stone in a vertical circle of radius \( 2 \, \text{m} \) has a speed of \( 12 \, \text{m/s} \) at the bottom. What is the tension at the top? (Take \( g = 10 \, \text{m/s}^2 \))

Q5. A \( 9.2 \, \text{kg} \) block on a horizontal surface (\( \mu_k = 0.2 \)) is pulled by a \( 7.2 \, \text{kg} \) mass over a pulley. A \( 20 \, \text{N} \) force opposes the \( 9.2 \, \text{kg} \) block. What is the tension? (Take \( g = 10 \, \text{m/s}^2 \))

Q6. A \( 1700 \, \text{kg} \) truck accelerates at \( 1.5 \, \text{m/s}^2 \) for \( 4 \, \text{s} \), then a \( 1.8 \, \text{kg} \) stone is dropped. What is the horizontal distance traveled by the stone in \( 2.5 \, \text{s} \)? (Neglect air resistance)

Q7. A body of mass \( 6 \, \text{kg} \) is acted upon by two perpendicular forces of \( 8 \, \text{N} \) and \( 6 \, \text{N} \). What is the magnitude of its acceleration?

Q8. A \( 50 \, \text{kg} \) man in a lift descending at \( 4 \, \text{m/s}^2 \) jumps upward with a speed of \( 5 \, \text{m/s} \) relative to the lift. What is the normal force on the floor during the jump? (Take \( g = 10 \, \text{m/s}^2 \))

Q9. A \( 0.48 \, \text{kg} \) stone in a vertical circle of radius \( 1.5 \, \text{m} \) has a tension of \( 32 \, \text{N} \) at the bottom. What is the tension at the top? (Take \( g = 10 \, \text{m/s}^2 \))

Q10. A \( 0.2 \, \text{kg} \) ball moving at \( 15 \, \text{m/s} \) strikes a wall perpendicularly and rebounds at \( 10 \, \text{m/s} \). What is the impulse? (Take \( g = 10 \, \text{m/s}^2 \))