MOTION IN A PLANE-QnA

Q1: What is a vector quantity?

A vector quantity is a physical quantity that requires both magnitude and direction for its complete description.

Q2: Name one scalar and one vector quantity.

Speed is a scalar quantity, while displacement is a vector quantity.

Q3: What is meant by a unit vector?

A unit vector is a vector having magnitude one and indicating direction only.

Q4: Which unit vector represents the positive y-direction?

The unit vector \(\mathbf{j}\) represents the positive y-direction.

Q5: What is the shape of the trajectory of a projectile?

The trajectory of a projectile is parabolic in shape.

Q6: What is the horizontal acceleration in projectile motion?

The horizontal acceleration in projectile motion is zero.

Q7: At what point is the vertical velocity of a projectile zero?

The vertical velocity is zero at the highest point of the projectile’s path.

Q8: What is uniform circular motion?

Uniform circular motion is motion along a circular path with constant speed.

Q9: In circular motion, the velocity is directed along which direction?

The velocity is always directed tangentially to the circular path.

Q10: What force keeps a body moving in a circular path?

The centripetal force keeps a body moving in a circular path.

Q11: Write the expression for centripetal acceleration.

The centripetal acceleration is given by \(a = \frac{v^2}{r}\).

Q12: Can the magnitude of velocity remain constant in circular motion?

Yes, the magnitude of velocity can remain constant while its direction changes.

Q13: What is the direction of centripetal acceleration?

It is directed towards the centre of the circular path.

Q14: What is meant by resolution of a vector?

Resolution of a vector is the process of breaking it into components along chosen directions.

Q15: Write the SI unit of angular velocity.

The SI unit of angular velocity is radian per second.

Q1: Explain why motion in a plane is called two-dimensional motion.

Motion in a plane is two-dimensional because the position of the object requires two perpendicular coordinates for complete description.

Q2: Why is projectile motion considered accelerated motion?

Projectile motion is accelerated because gravity continuously changes the vertical component of velocity.

Q3: State two characteristics of uniform circular motion.

Speed remains constant and acceleration always acts towards the centre of the circle.

Q4: What happens to the speed of a projectile at the highest point?

The speed does not become zero; only the vertical component becomes zero while horizontal component remains unchanged.

Q5: Write the relation between linear velocity and angular velocity.

Linear velocity is equal to the product of angular velocity and radius of the circular path.

Q6: Why does centripetal force do no work in circular motion?

Centripetal force is perpendicular to velocity, so it does not change the speed and hence does no work.

Q7: What determines the time of flight of a projectile?

The time of flight depends on the vertical component of initial velocity and gravity.

Q8: State the condition for maximum range of a projectile.

The range is maximum when the angle of projection is \(45^\circ\).

Q9: Why are horizontal and vertical motions independent in projectile motion?

Because gravity acts only vertically and does not affect horizontal motion.

Q1: Explain how vector addition is performed using the analytical method.

In the analytical method, vectors are resolved into x and y components, corresponding components are added algebraically, and the resultant is obtained from these sums.

Q2: Describe the motion of a body projected horizontally from a height.

The body moves with constant horizontal velocity while accelerating vertically due to gravity, producing a curved path.

Q3: Derive the expression for centripetal acceleration.

Centripetal acceleration arises due to continuous change in direction of velocity and is given by the ratio of square of speed to radius of the circular path.

Q4: Explain why a particle moving in a circle is always accelerated.

Even though speed may be constant, the direction of velocity changes continuously, resulting in acceleration.

Q5: Explain the significance of unit vectors in vector representation.

Unit vectors provide a standard way to express direction and simplify vector calculations in component form.

Q1: Explain projectile motion in detail with its key features.

Projectile motion is motion under gravity alone where horizontal motion is uniform and vertical motion is uniformly accelerated, resulting in a parabolic path.

Q2: Describe the concept of resolution of vectors and its importance.

Resolving vectors into perpendicular components simplifies analysis of motion and forces acting in different directions.

Q3: Discuss uniform circular motion and the role of centripetal force.

Uniform circular motion requires a centripetal force that continuously changes the direction of velocity to keep the body on a circular path.

Q4: Explain the independence of perpendicular motions with reference to projectile motion.

Horizontal and vertical motions act independently; one does not influence the other, allowing separate analysis along each axis.

Q5: Describe how vector methods help in understanding motion in a plane.

Vector methods allow precise representation of direction and magnitude, making complex two-dimensional motion easier to analyse mathematically.