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Q 01 / 25
A physical quantity that has only magnitude and no direction is called a scalar.
Q 02 / 25
Displacement in two dimensions is represented by a vector drawn from the final position to the initial position.
Q 03 / 25
The magnitude of a vector is always a non-negative real number.
Q 04 / 25
Two vectors are equal if and only if they have the same magnitude and the same direction, regardless of their initial points.
Q 05 / 25
Vector addition by the triangle method and by the parallelogram method always gives the same resultant.
Q 06 / 25
If two non-zero vectors are perpendicular to each other, the magnitude of their resultant is the sum of their magnitudes.
Q 07 / 25
A vector of given magnitude has a unique pair of rectangular components along any two fixed perpendicular directions.
Q 08 / 25
The x-component of a vector can be greater in magnitude than the vector itself.
Q 09 / 25
For any two vectors \(\vec{A}\) and \(\vec{B}\) in a plane, \(\vec{A}\cdot\vec{B}=0\) implies that the vectors are perpendicular.
Q 10 / 25
The cross product of two non-parallel vectors lying in the same plane is a vector perpendicular to that plane.
Q 11 / 25
In projectile motion on level ground (neglecting air resistance), the horizontal component of velocity remains constant throughout the motion.
Q 12 / 25
In projectile motion, the vertical component of velocity is the same at any two points that are at the same height above the ground.
Q 13 / 25
For a projectile launched with speed \(u\) at angle \(\theta\) above the horizontal, the time of flight on level ground is proportional to \(\cos\theta\).
Q 14 / 25
For fixed launch speed on level ground, the horizontal range of a projectile is maximum at a projection angle of \(45^\circ\).
Q 15 / 25
Two projectiles fired with the same speed at complementary angles \(\theta\) and \(90^\circ-\theta\) have the same maximum height.
Q 16 / 25
The trajectory of a projectile under uniform gravity and without air resistance is a parabola when described in Cartesian coordinates.
Q 17 / 25
In uniform circular motion, the speed and velocity of the particle both remain constant.
Q 18 / 25
In uniform circular motion of radius \(r\) and speed \(v\), the acceleration is always directed radially inward and has magnitude \(v^{2}/r\).
Q 19 / 25
A body moving in a circle with constant speed has zero tangential acceleration but non-zero normal (centripetal) acceleration.
Q 20 / 25
If the velocity of object B relative to object A is \(\vec{v}_{BA}\), then the velocity of A relative to B is \(-\vec{v}_{BA}\).
Q 21 / 25
In river-boat problems, if the boat is always steered perpendicular to the river bank, the shortest time to cross is achieved when the river flow speed is zero.
Q 22 / 25
The relative velocity of rain with respect to a moving observer can be found by subtracting the observer’s velocity vector from the rain’s velocity vector.
Q 23 / 25
For a projectile launched from ground and landing at a higher horizontal level, the equation \(R=\dfrac{u^{2}\sin 2\theta}{g}\) for range on level ground remains valid without modification.
Q 24 / 25
In uniform circular motion, if the angular speed of a particle is doubled while the radius is halved, the magnitude of its centripetal acceleration remains unchanged.
Q 25 / 25
For a projectile launched with speed \(u\) at angle \(\theta\), if its horizontal range on level ground is equal to its maximum height, then \(\tan\theta=8\).

Frequently Asked Questions

Motion in a plane is motion of a particle in two dimensions, where its position, velocity, and acceleration are represented by vectors in an \(x\text{-}y\) plane.

A scalar quantity is one that has only magnitude and no direction, such as mass, distance, speed, time, or temperature.

A vector quantity has both magnitude and direction, such as displacement, velocity, acceleration, and force.

Position vector \(\vec{r}\) of a particle at \((x,y)\) is given by \(\vec{r}=x\hat{i}+y\hat{j}\) with respect to the origin \(O(0,0)\).

Displacement vector is the change in position: \(\Delta\vec{r}=\vec{r}_2-\vec{r}_1\), independent of the actual path followed.

Average velocity is \(\vec{v}_{\text{avg}}=\frac{\Delta\vec{r}}{\Delta t}\), where \(\Delta\vec{r}\) is displacement in time interval \(\Delta t\).

Instantaneous velocity is \(\vec{v}=\frac{d\vec{r}}{dt}\) and is always tangent to the path at that instant.

Average acceleration is \(\vec{a}_{\text{avg}}=\frac{\Delta\vec{v}}{\Delta t}\), where \(\Delta\vec{v}\) is change in velocity in time \(\Delta t\).

Instantaneous acceleration is \(\vec{a}=\frac{d\vec{v}}{dt}\) and measures the rate of change of velocity vector at a given instant.

If two vectors are represented by two sides of a triangle taken in order, the third side taken in the same order represents their resultant.

If two vectors from the same point form adjacent sides of a parallelogram, the diagonal through that point gives the resultant vector.

For vectors \(\vec{A}\) and \(\vec{B}\) with angle \(\theta\) between them, resultant magnitude is \(R=\sqrt{A^2+B^2+2AB\cos\theta}\).

Vector subtraction \(\vec{A}-\vec{B}\) is defined as \(\vec{A}+(-\vec{B})\), where \(-\vec{B}\) has same magnitude as \(\vec{B}\) but opposite direction.

A unit vector has magnitude 1 and gives only direction; unit vector along \(\vec{A}\) is \(\hat{A}=\frac{\vec{A}}{|\vec{A}|}\)

If \(\vec{A}\) makes angle \(\theta\) with positive \(x\)-axis, then \(A_x=A\cos\theta\), \(A_y=A\sin\theta\), and \(\vec{A}=A_x\hat{i}+A_y\hat{j}\).
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