NEET Laws of Motion — Set 14

Question 1

A stone of mass $ 0.3 \, \text{kg} $ is whirled in a horizontal circle of radius $ 2 \, \text{m} $ at $ 20 \, \text{rev/min} $. What is the tension in the string?

Accepted Answer

Tension provides the centripetal force $ F = m \omega^2 r $. Convert revolutions to angular speed: $ \omega = 20 \, \text{rev/min} = \frac{20 \times 2\pi}{60} = \frac{2\pi}{3} \, \text{rad/s} $. Calculate $ \omega^2 = \left(\frac{2\pi}{3}\right)^2 = \frac{4\pi^2}{9} $. Substitute: $ m = 0.3 \, \text{kg} $, $ r = 2 \, \text{m} $. So, $ F = 0.3 \times \frac{4\pi^2}{9} \times 2 = 0.3 \times \frac{8\pi^2}{9} \approx 2.63 \, \text{N} $.

Question 2

A $ 5 \, \text{kg} $ block on a horizontal surface ($ \mu_k = 0.3 $) is connected to a $ 3 \, \text{kg} $ mass over a pulley. A force of $ 20 \, \text{N} $ at $ 60^\circ $ to the horizontal pulls the $ 5 \, \text{kg} $ block. What is the acceleration? (Take $ g = 10 \, \text{m/s}^2 $, $ \sin 60^\circ = 0.866 $, $ \cos 60^\circ = 0.5 $)

Accepted Answer

For $ 3 \, \text{kg} $: $ 3g - T = 3a \Rightarrow 30 - T = 3a $. For $ 5 \, \text{kg} $: $ T + F \cos 60^\circ - f_k = 5a $, $ N = mg - F \sin 60^\circ $. $ N = 5 \times 10 - 20 \times 0.866 = 50 - 17.32 = 32.68 \, \text{N} $. $ f_k = 0.3 \times 32.68 \approx 9.8 \, \text{N} $, $ F \cos 60^\circ = 20 \times 0.5 = 10 \, \text{N} $. $ T + 10 - 9.8 = 5a \Rightarrow T + 0.2 = 5a $. Solve: $ 30 - T = 3a $, $ T + 0.2 = 5a \Rightarrow 30 - (5a - 0.2) = 3a \Rightarrow 30.2 = 8a \Rightarrow a \approx 3.78 \, \text{m/s}^2 $.

Question 3

A $ 55 \, \text{kg} $ man in a lift accelerating upward at $ 1 \, \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 $. $ N - 55 \times 10 = 55 \times 1 $. $ N - 550 = 55 \Rightarrow N = 605 \, \text{N} $.

NEET Physics: Laws of Motion — Practice Set 14

Q1. A stone of mass \( 0.3 \, \text{kg} \) is whirled in a horizontal circle of radius \( 2 \, \text{m} \) at \( 20 \, \text{rev/min} \). What is the tension in the string?

Q3. A \( 55 \, \text{kg} \) man in a lift accelerating upward at \( 1 \, \text{m/s}^2 \) stands on a scale. What is the reading? (Take \( g = 10 \, \text{m/s}^2 \))

Q5. A \( 0.36 \, \text{kg} \) stone is whirled in a horizontal circle of radius \( 1.7 \, \text{m} \) with a tension of \( 14 \, \text{N} \). What is the speed? (Take \( g = 10 \, \text{m/s}^2 \))

Q7. A \( 0.5 \, \text{kg} \) stone is whirled in a vertical circle of radius \( 2 \, \text{m} \) at \( 30 \, \text{rev/min} \). What is the tension at the top? (Take \( g = 10 \, \text{m/s}^2 \))

Q8. A car of mass \( 800 \, \text{kg} \) takes a circular turn of radius \( 20 \, \text{m} \) at \( 10 \, \text{m/s} \) on a level road. What is the frictional force providing the centripetal force?

Q9. A \( 0.1 \, \text{kg} \) ball moving at \( 20 \, \text{m/s} \) hits a wall at \( 30^\circ \) and rebounds at the same speed and angle. What is the impulse along the wall? (Take \( \sin 30^\circ = 0.5 \), \( \cos 30^\circ = 0.866 \))