NEET Laws of Motion — Set 5

Question 1

Two billiard balls, each of mass $ 0.1 \, \text{kg} $, moving in opposite directions at $ 5 \, \text{m/s} $, collide and rebound with the same speed. What is the impulse on one ball due to the other?

Accepted Answer

Impulse = change in momentum of one ball. For one ball: initial momentum $ p_i = 0.1 \times 5 = 0.5 \, \text{kg m/s} $. After collision (rebounds): $ p_f = 0.1 \times (-5) = -0.5 \, \text{kg m/s} $. Change $ \Delta p = p_f - p_i = -0.5 - 0.5 = -1 \, \text{kg m/s} $. Magnitude of impulse = $ 1 \, \text{N s} $.

Question 2

A $ 1300 \, \text{kg} $ car turns on a banked road ($ \theta = 15^\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 15^\circ \approx 0.268 $)

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 15^\circ = 0.268 $. $ v_0^2 = 50 \times 10 \times 0.268 = 500 \times 0.268 = 134 $. $ v_0 = \sqrt{134} \approx 11.58 \, \text{m/s} $.

Question 3

A $ 50 \, \text{kg} $ man in a lift accelerating upward at $ 2 \, \text{m/s}^2 $ stands on a scale. What is the reading? (Take $ g = 10 \, \text{m/s}^2 $)

Accepted Answer

The scale reads the normal force, which is the apparent weight. Net force: $ N - mg = ma $. Substitute: $ N - 50 \times 10 = 50 \times 2 $. $ N - 500 = 100 \Rightarrow N = 600 \, \text{N} $. The reading is $ 600 \, \text{N} $.

NEET Physics: Laws of Motion — Practice Set 5

Q1. Two billiard balls, each of mass \( 0.1 \, \text{kg} \), moving in opposite directions at \( 5 \, \text{m/s} \), collide and rebound with the same speed. What is the impulse on one ball due to the other?

Q2. A \( 1300 \, \text{kg} \) car turns on a banked road (\( \theta = 15^\circ \)) with radius \( 50 \, \text{m} \) at the optimum speed to avoid friction. What is the speed? (Take \( g = 10 \, \text{m/s}^2 \), \( \tan 15^\circ \approx 0.268 \))

Q3. A \( 50 \, \text{kg} \) man in a lift accelerating upward at \( 2 \, \text{m/s}^2 \) stands on a scale. What is the reading? (Take \( g = 10 \, \text{m/s}^2 \))

Q4. A \( 2500 \, \text{kg} \) rocket accelerates at \( 8 \, \text{m/s}^2 \) upward while ejecting gas at \( 50 \, \text{kg/s} \) with speed \( 100 \, \text{m/s} \) relative to the rocket. What is the total thrust? (Take \( g = 10 \, \text{m/s}^2 \))

Q5. A \( 60 \, \text{kg} \) man in a lift accelerating upward at \( 1.5 \, \text{m/s}^2 \) stands on a scale. What is the reading? (Take \( g = 10 \, \text{m/s}^2 \))

Q6. A \( 0.3 \, \text{kg} \) ball moving at \( 20 \, \text{m/s} \) at \( 30^\circ \) to a wall rebounds at the same speed and angle. What is the impulse magnitude? (Take \( \sin 30^\circ = 0.5 \), \( \cos 30^\circ = 0.866 \))

Q7. A wooden block of mass \( 3 \, \text{kg} \) on a soft floor sinks with an acceleration of \( 0.2 \, \text{m/s}^2 \) when a \( 27 \, \text{kg} \) mass is placed on it. What is the normal force on the floor? (Take \( g = 10 \, \text{m/s}^2 \))

Q8. A \( 5.4 \, \text{kg} \) block on a horizontal surface (\( \mu_k = 0.25 \)) is connected to a \( 7.4 \, \text{kg} \) mass over a pulley. A \( 17 \, \text{N} \) force opposes the \( 5.4 \, \text{kg} \) block. What is the acceleration? (Take \( g = 10 \, \text{m/s}^2 \))

Q9. A \( 7.2 \, \text{kg} \) block on a horizontal surface (\( \mu_k = 0.3 \)) is pulled by a \( 5.2 \, \text{kg} \) mass over a pulley. A \( 18 \, \text{N} \) force opposes the \( 7.2 \, \text{kg} \) block. What is the tension? (Take \( g = 10 \, \text{m/s}^2 \))

Q10. A \( 75 \, \text{kg} \) man in a lift accelerating downward at \( 2 \, \text{m/s}^2 \) stands on a scale. What is the reading? (Take \( g = 10 \, \text{m/s}^2 \))