NEET Laws of Motion — Set 11

Question 1

A $ 0.4 \, \text{kg} $ ball at $ 40 \, \text{m/s} $ hits a wall at $ 45^\circ $ and rebounds at $ 30^\circ $ with speed $ 35 \, \text{m/s} $. What is the impulse along the wall? (Take $ \sin 45^\circ = \cos 45^\circ = 0.707 $, $ \sin 30^\circ = 0.5 $, $ \cos 30^\circ = 0.866 $)

Accepted Answer

Along wall (y-axis): Initial $ p_y = 0.4 \times 40 \times 0.707 = 11.31 \, \text{kg m/s} $. Final $ p_y = 0.4 \times 35 \times 0.5 = 7 \, \text{kg m/s} $. Impulse $ \Delta p_y = 7 - 11.31 = -4.31 \, \text{N s} $. Magnitude = $ 4.31 \, \text{N s} $.

Question 2

A $ 1000 \, \text{kg} $ car on a $ 30^\circ $ banked road ($ \mu_s = 0.35 $) turns at radius $ 50 \, \text{m} $ while decelerating at $ 2 \, \text{m/s}^2 $ tangentially. What is the maximum speed? (Take $ g = 10 \, \text{m/s}^2 $, $ \tan 30^\circ = 0.577 $)

Accepted Answer

Max speed: $ v_{\text{max}} = \sqrt{rg \frac{\mu_s + \tan\theta}{1 - \mu_s \tan\theta}} $. $ \mu_s + \tan\theta = 0.35 + 0.577 = 0.927 $, $ 1 - 0.35 \times 0.577 = 1 - 0.20195 = 0.79805 $. $ v_{\text{max}}^2 = 50 \times 10 \times \frac{0.927}{0.79805} \approx 500 \times 1.161 \approx 580.5 $. $ v_{\text{max}} \approx \sqrt{580.5} \approx 24.09 \, \text{m/s} $. Tangential deceleration doesn’t affect radial max speed.

Question 3

A $ 3.5 \, \text{kg} $ block on a horizontal surface ($ \mu_k = 0.25 $) is connected to a $ 5.5 \, \text{kg} $ mass over a pulley. A $ 8 \, \text{N} $ force aids the $ 3.5 \, \text{kg} $ block. What is the acceleration? (Take $ g = 10 \, \text{m/s}^2 $)

Accepted Answer

The $ 5.5 \, \text{kg} $ mass descends, pulling the $ 3.5 \, \text{kg} $ block horizontally with an aiding force. For $ 5.5 \, \text{kg} $: $ 5.5g - T = 5.5a \Rightarrow 55 - T = 5.5a $. For $ 3.5 \, \text{kg} $: $ T + 8 - f_k = 3.5a $. Normal force: $ N = mg = 3.5 \times 10 = 35 \, \text{N} $. Friction: $ f_k = 0.25 \times 35 = 8.75 \, \text{N} $. Net force: $ T + 8 - 8.75 = 3.5a \Rightarrow T - 0.75 = 3.5a $. Solve: $ 55 - T = 5.5a $, $ T - 0.75 = 3.5a $. Substitute: $ 55 - (3.5a + 0.75) = 5.5a \Rightarrow 55 - 0.75 - 3.5a = 5.5a \Rightarrow 54.25 = 9a $. $ a = \frac{54.25}{9} \approx 6.03 \, \text{m/s}^2 $.

NEET Physics: Laws of Motion — Practice Set 11

Q1. A \( 0.4 \, \text{kg} \) ball at \( 40 \, \text{m/s} \) hits a wall at \( 45^\circ \) and rebounds at \( 30^\circ \) with speed \( 35 \, \text{m/s} \). What is the impulse along the wall? (Take \( \sin 45^\circ = \cos 45^\circ = 0.707 \), \( \sin 30^\circ = 0.5 \), \( \cos 30^\circ = 0.866 \))

Q2. A \( 1000 \, \text{kg} \) car on a \( 30^\circ \) banked road (\( \mu_s = 0.35 \)) turns at radius \( 50 \, \text{m} \) while decelerating at \( 2 \, \text{m/s}^2 \) tangentially. What is the maximum speed? (Take \( g = 10 \, \text{m/s}^2 \), \( \tan 30^\circ = 0.577 \))

Q3. A \( 3.5 \, \text{kg} \) block on a horizontal surface (\( \mu_k = 0.25 \)) is connected to a \( 5.5 \, \text{kg} \) mass over a pulley. A \( 8 \, \text{N} \) force aids the \( 3.5 \, \text{kg} \) block. What is the acceleration? (Take \( g = 10 \, \text{m/s}^2 \))

Q5. A \( 7.6 \, \text{kg} \) block on a \( 60^\circ \) incline (\( \mu_k = 0.15 \)) is pulled upward by a \( 9.6 \, \text{kg} \) mass over a pulley. What is the acceleration? (Take \( g = 10 \, \text{m/s}^2 \), \( \sin 60^\circ = 0.866 \), \( \cos 60^\circ = 0.5 \))

Q7. A \( 4000 \, \text{kg} \) rocket accelerates upward at \( 5 \, \text{m/s}^2 \) while ejecting gas at \( 80 \, \text{kg/s} \) with speed \( 120 \, \text{m/s} \) relative to the rocket. What is the total thrust? (Take \( g = 10 \, \text{m/s}^2 \))

Q8. A \( 8.5 \, \text{kg} \) block on a horizontal surface (\( \mu_k = 0.25 \)) is pulled by a \( 4.5 \, \text{kg} \) mass over a pulley. A \( 15 \, \text{N} \) force opposes the \( 8.5 \, \text{kg} \) block. What is the acceleration? (Take \( g = 10 \, \text{m/s}^2 \))

Q9. A \( 0.7 \, \text{kg} \) stone in a vertical circle of radius \( 2.5 \, \text{m} \) has a tension of \( 25 \, \text{N} \) at the bottom and \( 5 \, \text{N} \) at the top. What is the tangential acceleration? (Take \( g = 10 \, \text{m/s}^2 \))