NEET Laws of Motion — Set 16

Question 1

A $ 45 \, \text{kg} $ man in a lift accelerating downward 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 $, where $ a = -1.5 \, \text{m/s}^2 $. $ N - 45 \times 10 = 45 \times (-1.5) $. $ N - 450 = -67.5 \Rightarrow N = 382.5 \, \text{N} $.

Question 2

A $ 1900 \, \text{kg} $ rocket accelerates upward at $ 2.5 \, \text{m/s}^2 $ with a thrust of $ 25000 \, \text{N} $. What is the mass ejection rate if the gas speed is $ 90 \, \text{m/s} $ relative to the rocket? (Take $ g = 10 \, \text{m/s}^2 $)

Accepted Answer

Net force: $ T - mg = ma $. $ 25000 - 1900 \times 10 = 1900 \times 2.5 \Rightarrow 25000 - 19000 = 4750 $. Net force from ejection: $ T_{\text{ejection}} = ma = 4750 \, \text{N} $. Thrust from gas: $ T_{\text{ejection}} = \frac{dm}{dt} \times v_{\text{rel}} $. $ 4750 = \frac{dm}{dt} \times 90 \Rightarrow \frac{dm}{dt} = \frac{4750}{90} \approx 52.78 \, \text{kg/s} $.

Question 3

A $ 3 \, \text{kg} $ block on a $ 30^\circ $ incline ($ \mu_s = 0.4 $) is pushed up by a force parallel to the incline just enough to start motion. What is the force? (Take $ g = 10 \, \text{m/s}^2 $, $ \sin 30^\circ = 0.5 $, $ \cos 30^\circ = 0.866 $)

Accepted Answer

Upward motion: $ F - mg \sin\theta - f_s = 0 $ at impending motion. $ f_s = \mu_s N $, $ N = mg \cos\theta = 3 \times 10 \times 0.866 = 25.98 \, \text{N} $. $ f_s = 0.4 \times 25.98 \approx 10.39 \, \text{N} $. $ mg \sin\theta = 3 \times 10 \times 0.5 = 15 \, \text{N} $. $ F = 15 + 10.39 = 25.39 \, \text{N} \approx 25.4 \, \text{N} $.

NEET Physics: Laws of Motion — Practice Set 16

Q1. A \( 45 \, \text{kg} \) man in a lift accelerating downward at \( 1.5 \, \text{m/s}^2 \) stands on a scale. What is the reading? (Take \( g = 10 \, \text{m/s}^2 \))

Q2. A \( 1900 \, \text{kg} \) rocket accelerates upward at \( 2.5 \, \text{m/s}^2 \) with a thrust of \( 25000 \, \text{N} \). What is the mass ejection rate if the gas speed is \( 90 \, \text{m/s} \) relative to the rocket? (Take \( g = 10 \, \text{m/s}^2 \))

Q3. A \( 3 \, \text{kg} \) block on a \( 30^\circ \) incline (\( \mu_s = 0.4 \)) is pushed up by a force parallel to the incline just enough to start motion. What is the force? (Take \( g = 10 \, \text{m/s}^2 \), \( \sin 30^\circ = 0.5 \), \( \cos 30^\circ = 0.866 \))

Q4. A \( 2.6 \, \text{kg} \) block on a \( 30^\circ \) incline (\( \mu_s = 0.35 \)) is pulled downward by a horizontal force just sufficient to start motion. What is the force? (Take \( g = 10 \, \text{m/s}^2 \), \( \sin 30^\circ = 0.5 \), \( \cos 30^\circ = 0.866 \))

Q5. A \( 400 \, \text{kg} \) vehicle decelerates from \( 20 \, \text{m/s} \) to rest in \( 5 \, \text{s} \). What is the average force applied?

Q6. A bullet of mass \( 0.05 \, \text{kg} \) moving at \( 100 \, \text{m/s} \) is stopped by a wooden block in \( 0.5 \, \text{m} \). What is the average resistive force exerted by the block on the bullet?

Q7. A \( 1500 \, \text{kg} \) truck accelerates at \( 2 \, \text{m/s}^2 \) for \( 5 \, \text{s} \), then a \( 1 \, \text{kg} \) stone is dropped. What is the horizontal distance traveled by the stone in \( 1 \, \text{s} \)? (Neglect air resistance)

Q8. A \( 0.6 \, \text{kg} \) stone in a vertical circle of radius \( 1.5 \, \text{m} \) has a speed of \( 10 \, \text{m/s} \) at the bottom. What is the tension at the top? (Take \( g = 10 \, \text{m/s}^2 \))

Q9. A block of mass \( 8 \, \text{kg} \) rests on a horizontal plane. The plane is inclined at \( 30^\circ \) when the block just begins to slide. What is the coefficient of static friction?

Q10. A bob of mass \( 0.2 \, \text{kg} \) hangs from a \( 1 \, \text{m} \) string. If the string is cut at its mean position with speed \( 2 \, \text{m/s} \), what is its initial horizontal velocity?