NEET Laws of Motion — Set 2

Question 1

A $ 0.4 \, \text{kg} $ stone in a vertical circle of radius $ 2 \, \text{m} $ has a tension of $ 20 \, \text{N} $ at the bottom. What is the tension at the top? (Take $ g = 10 \, \text{m/s}^2 $)

Accepted Answer

At bottom: $ T_b - mg = m v_b^2 / r \Rightarrow 20 - 0.4 \times 10 = 0.4 \times v_b^2 / 2 $. $ 20 - 4 = 0.2 v_b^2 \Rightarrow 16 = 0.2 v_b^2 \Rightarrow v_b^2 = 80 \Rightarrow v_b \approx 8.94 \, \text{m/s} $. Energy conservation: $ \frac{1}{2} m v_b^2 = \frac{1}{2} m v_t^2 + 2mg $ (no tangential force). $ 0.5 \times 0.4 \times 80 = 0.5 \times 0.4 \times v_t^2 + 2 \times 0.4 \times 10 $. $ 16 = 0.2 v_t^2 + 8 \Rightarrow 0.2 v_t^2 = 8 \Rightarrow v_t^2 = 40 \Rightarrow v_t \approx 6.32 \, \text{m/s} $. At top: $ T_t + mg = m v_t^2 / r \Rightarrow T_t + 4 = 0.4 \times 40 / 2 \Rightarrow T_t + 4 = 8 \Rightarrow T_t = 4 \, \text{N} $.

Question 2

A $ 60 \, \text{kg} $ man stands in a lift that accelerates downward at $ 3 \, \text{m/s}^2 $ and then jumps with an upward acceleration of $ 7 \, \text{m/s}^2 $ relative to the lift. What is the normal force during the jump? (Take $ g = 10 \, \text{m/s}^2 $)

Accepted Answer

Relative to ground: $ a_{\text{net}} = a_{\text{jump}} + a_{\text{lift}} = 7 + (-3) = 4 \, \text{m/s}^2 $ upward. $ N - mg = ma_{\text{net}} $. $ N - 60 \times 10 = 60 \times 4 $. $ N - 600 = 240 \Rightarrow N = 840 \, \text{N} $.

Question 3

A $ 0.5 \, \text{kg} $ stone tied to a string of length $ 1 \, \text{m} $ is whirled at $ 60 \, \text{rev/min} $. What is the maximum tension the string can withstand if it breaks at $ 50 \, \text{N} $?

Accepted Answer

Centripetal force $ F = m \omega^2 r $. $ \omega = 60 \, \text{rev/min} = \frac{60 \times 2\pi}{60} = 2\pi \, \text{rad/s} $. $ \omega^2 = (2\pi)^2 = 4\pi^2 $. $ F = 0.5 \times 4\pi^2 \times 1 \approx 19.74 \, \text{N} $. Since $ 19.74 \, \text{N} < 50 \, \text{N} $, maximum tension possible here is $ 50 \, \text{N} $ (breaking limit).

NEET Physics: Laws of Motion — Practice Set 2

Q1. A \( 0.4 \, \text{kg} \) stone in a vertical circle of radius \( 2 \, \text{m} \) has a tension of \( 20 \, \text{N} \) at the bottom. What is the tension at the top? (Take \( g = 10 \, \text{m/s}^2 \))

Q2. A \( 60 \, \text{kg} \) man stands in a lift that accelerates downward at \( 3 \, \text{m/s}^2 \) and then jumps with an upward acceleration of \( 7 \, \text{m/s}^2 \) relative to the lift. What is the normal force during the jump? (Take \( g = 10 \, \text{m/s}^2 \))

Q3. A \( 0.5 \, \text{kg} \) stone tied to a string of length \( 1 \, \text{m} \) is whirled at \( 60 \, \text{rev/min} \). What is the maximum tension the string can withstand if it breaks at \( 50 \, \text{N} \)?

Q4. A \( 1600 \, \text{kg} \) truck accelerates at \( 3 \, \text{m/s}^2 \) for \( 3 \, \text{s} \), then a \( 1.5 \, \text{kg} \) stone is dropped. What is the horizontal distance traveled by the stone in \( 2 \, \text{s} \)? (Neglect air resistance)

Q5. A \( 10 \, \text{kg} \) mass is suspended by a rope with a \( 40 \, \text{N} \) horizontal force at its midpoint. What is the angle the rope makes with the vertical? (Take \( g = 10 \, \text{m/s}^2 \))

Q7. A \( 0.35 \, \text{kg} \) stone is whirled in a horizontal circle of radius \( 1.2 \, \text{m} \) at \( 50 \, \text{rev/min} \). What is the tension? (Take \( g = 10 \, \text{m/s}^2 \))

Q8. A \( 85 \, \text{kg} \) man in a lift accelerating upward at \( 1.8 \, \text{m/s}^2 \) stands on a scale. What is the reading? (Take \( g = 10 \, \text{m/s}^2 \))

Q9. A body of mass \( 10 \, \text{kg} \) is on a horizontal surface with a coefficient of static friction \( 0.2 \). What is the maximum static frictional force? (Take \( g = 10 \, \text{m/s}^2 \))

Q10. A \( 0.25 \, \text{kg} \) ball moving at \( 18 \, \text{m/s} \) at \( 53^\circ \) to a wall rebounds at the same speed and angle. What is the impulse perpendicular to the wall? (Take \( \sin 53^\circ = 0.8 \), \( \cos 53^\circ = 0.6 \))

Q11. A \( 8.4 \, \text{kg} \) block on a horizontal surface (\( \mu_k = 0.25 \)) is pulled by a \( 6.4 \, \text{kg} \) mass over a pulley. A \( 19 \, \text{N} \) force opposes the \( 8.4 \, \text{kg} \) block. What is the tension? (Take \( g = 10 \, \text{m/s}^2 \))

Q12. A \( 1 \, \text{kg} \) stone in a vertical circle of radius \( 4 \, \text{m} \) has a speed of \( 20 \, \text{m/s} \) at the bottom. A tangential force of \( 4 \, \text{N} \) acts downward from bottom to top. What is the tension at the top? (Take \( g = 10 \, \text{m/s}^2 \))

Q13. A \( 0.38 \, \text{kg} \) stone in a vertical circle of radius \( 1.9 \, \text{m} \) has a tension of \( 28 \, \text{N} \) at the bottom. What is the tension at the top? (Take \( g = 10 \, \text{m/s}^2 \))