The moment of a force about a point is calculated as the product of the force and the perpendicular distance from the point to the line of action of the force.
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Q2. What is the center of gravity of a uniform beam of length L?
Solution:
For a uniform beam, the center of gravity is located at its midpoint, which is L/2.
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Q3. In a static system, if the sum of vertical forces is zero and the sum of horizontal forces is also zero, what can be concluded?
Solution:
If the sum of vertical and horizontal forces is zero, the system is in static equilibrium.
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Q4. What is the acceleration of an object in free fall near the Earth's surface?
Solution:
The acceleration due to gravity near the Earth's surface is approximately 9.81 m/s².
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Q5. A ball is thrown vertically upwards with a speed of 20 m/s. How high will it go before it starts to fall back down? (g = 10 m/s²)
Solution:
Using the formula v² = u² + 2as, where v = 0, u = 20 m/s, and a = -10 m/s², we get 0 = 20² + 2 * (-10) * s, solving gives s = 20 m.
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Q6. A car moving at 60 km/h applies brakes and comes to a stop in 5 seconds. What is the distance covered during braking?
Solution:
Convert speed to m/s: 60 km/h = 16.67 m/s. Using s = ut + 0.5at², where a = (0 - 16.67)/5 = -3.33 m/s², we find s = 16.67 * 5 + 0.5 * (-3.33) * 5² = 41.67 m.
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Q7. A block on an inclined plane has a mass of 10 kg and the angle of inclination is 30 degrees. What is the force of friction if the coefficient of kinetic friction is 0.2?
Solution:
The normal force N = mg * cos(θ) = 10 kg * 9.81 m/s² * cos(30°) ≈ 84.87 N. The force of friction Ff = μk * N = 0.2 * 84.87 N ≈ 16.97 N.
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Q8. A car accelerates from rest at a rate of 2 m/s². How far does it travel in 5 seconds?
Solution:
Using the formula s = ut + 0.5at², where u = 0, a = 2 m/s², and t = 5 s, we get s = 0 + 0.5 * 2 * 5² = 25 m.
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Q9. If a car accelerates from rest at a rate of 2 m/s², what is its velocity after 5 seconds?
Solution:
Using the formula v = u + at, where u = 0, a = 2 m/s², and t = 5 s, we get v = 0 + (2)(5) = 10 m/s.
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Q10. A car travels 100 meters in 4 seconds. What is its average speed?
Solution:
Average speed = total distance / total time = 100 m / 4 s = 25 m/s.
