1. A body is thrown horizontally from a height. Neglecting air resistance, its trajectory will be:
Answer:
Explanation:
When a body is thrown horizontally and allowed to move under gravity, its path is parabolic.
2. A vector of magnitude 5 units is added to a vector of magnitude 12 units. What is the maximum possible magnitude of the resultant vector?
Answer:
Explanation:
Maximum magnitude of resultant = Sum of magnitudes of the two vectors = 5 + 12 = 17 units.
3. Two vectors are said to be perpendicular if their dot product is:
Answer:
Explanation:
Dot product of perpendicular vectors is zero.
4. Which of the following is a scalar quantity?
Answer:
Explanation:
Speed has only magnitude and no direction.
5. A particle moves in a plane under the action of a force. If its linear momentum is constant, then the force acting on it:
Answer:
Explanation:
A constant momentum indicates no net force acting on the particle.
6. The angle between two vectors A and B is 60 degrees. If A.B = 50, then what is |A| x |B|?
Answer:
Explanation:
A.B = |A| x |B| x cos(θ). Given A.B = 50 and θ = 60°, solving gives |A| x |B| = 50√3.
7. Which of the following motions is not an example of motion in a plane?
Answer:
Explanation:
A car moving on a straight road is an example of motion in a straight line, not in a plane.
8. A vector of magnitude 10 units is resolved into two components at 90 degrees to each other. If one component is 6 units, the other component is:
Answer:
Explanation:
By Pythagoras theorem, the other component = sqrt(10^2 – 6^2) = 8 units.
9. An airplane flies 200 km due west and then 200 km due north. The magnitude of the resultant displacement is:
Answer:
Explanation:
Using the Pythagoras theorem, the resultant = sqrt(200^2 + 200^2) = 282.8 km.
10. If vector A = 2i + 3j and vector B = i + 4j, then the magnitude of the resultant vector A + B is:
Answer:
Explanation:
A + B = (2i + i) + (3j + 4j) = 3i + 7j. Magnitude = sqrt(3^2 + 7^2) = 4.24 units.
11. A particle moves in a circular path of radius 5m with a constant speed of 10m/s. The acceleration of the particle is:
Answer:
Explanation:
For uniform circular motion, acceleration (centripetal) = v^2/r = 10^2/5 = 2 m/s^2.
12. A particle moves in the XY plane according to the equations x = a sin(ωt) and y = a cos(ωt). The path of the particle is:
Answer:
Explanation:
From the given equations, x^2/a^2 + y^2/a^2 = sin^2(ωt) + cos^2(ωt) = 1, which is the equation of a circle.
13. Two vectors of magnitudes 5 units and 12 units cannot be combined to give a resultant of:
Answer:
Explanation:
The minimum magnitude of resultant = |12 – 5| = 7 units. So, it's not possible to get a resultant lesser than this value by combining the vectors.
14. The time period of revolution of a particle in a circular orbit of radius 'r' with a constant speed 'v' is:
Answer:
Explanation:
Time period = Total path length / speed = 2πr/v.
15. Which of the following is true regarding vectors?
Answer:
Explanation:
By definition, vectors have both magnitude and direction.