The speed at the maximum height of a projectile is half of its initial speed $u$. The horizontal range of projectile is
- A$\frac{3 u^2}{2 g}$
- B$\frac{\sqrt{3} u^2}{2 g}$
- C$\frac{u^2}{2 g}$
- D$\frac{2 u^2}{g}$
Question types
PART - 1 CH - 3 Motion in a Plane question types
130 questions across 9 question groups — pick any mix to generate a Physics paper with step-by-step answer keys.
130
Questions
9
Question groups
5
Question types
01
M.C.Q (1 Marks)
12 Q→02Fill In The Blanks[1 Marks ]
10 Q→03True False[1 Marks ]
10 Q→041 Marks Question
44 Q→052 Marks Questions
17 Q→063 Marks Question
16 Q→074 Marks Question
3 Q→08Match the following.
2 Q→095 Marks Questions
16 Q→Sample Questions
PART - 1 CH - 3 Motion in a Plane questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If the vector is a unit vector in the direction of A. So
- ✓$\hat{n}=\frac{\vec{A}}{|\vec{A}|}$
- B$\hat{n}=\frac{|\vec{A}|}{\vec{A}}$
- C$\hat{n}=|\overrightarrow{ A }||\overrightarrow{ A }|$
- D$\hat{n}=\hat{n} \times \overrightarrow{ A }$
Answer: A.
View full solution →Two forces of 2 and 3 newton are acting perpendicular to each other on a particle. Their resultant force will make an angle with the force of 3 newton
- A$2 / 3$
- ✓$\tan ^{-1}\left(\frac{2}{3}\right)$
- C
- D$\tan ^{-1}\left(\frac{3}{2}\right)$
Answer: B.
View full solution →In how many directions (at angles) can a body be projected with the same speed for the same range?
- ✓2
- B3
- C4
- D1
Answer: A.
View full solution →The path of projectile is
- ARectilinear
- ✓Parabolic
- CElliptical
- DHyperbolic
Answer: B.
View full solution →A body can be projected in.............different directions (angles) with the same speed for the same horizontal range.
For maximum horizontal range of an object, the angle of projection should be ................ .
The tangential acceleration of a particle moving with constant speed in a circular of path radius R will be ............... .
Time of flight of the projectile T ............... .
Maximum height (H) max is ............... .
The motion of an ant on a paper is motion in a plane
Maximum range, $R =\frac{u}{g}$
View full solution →The angle between resultant vector $\vec{R}$ and $\vec{P}$ is,
$
\alpha=\tan ^{-1}\left(\frac{Q \sin \theta}{P+Q \cos \theta}\right)
$
View full solution →$
\alpha=\tan ^{-1}\left(\frac{Q \sin \theta}{P+Q \cos \theta}\right)
$
For maximum range, $\theta=45^{\circ}$
View full solution →In projectiles with uniform speed, the range is not the same in cases when $\theta=40^{\circ}$ and $\theta=50^{\circ}$
View full solution →Pick out the only vector quantity in the following list :
Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction, charge.
Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction, charge.
For any arbitrary motion in space, which of the following relations are true?
(a) $\vec{v}_{\text {avg }}=(1 / 2)\left[\vec{v}\left(t_1\right)+\vec{v}\left(t_2\right)\right]$
(b) $\vec{v}_{ avg }=\left[\vec{r}\left(t_2\right)-\vec{r}\left(t_1\right)\right] /\left(t_2-t_1\right)$
(c) $\vec{v}(t)=\vec{v}(0)+\vec{a} t$
(d) $\vec{r}( t )=\vec{r}(0)+\vec{v}(0) t+(1 / 2) \vec{a} t^2$
(e) $\vec{a}_{\text {avg }}=\left[\vec{v}\left(t_2\right)-\vec{v}\left(t_1\right)\right] /\left(t_2-t_1\right)$
Here, 'average' means the average values of physical quantities related to the time interval $t_2$ and $t_1$.
View full solution →(a) $\vec{v}_{\text {avg }}=(1 / 2)\left[\vec{v}\left(t_1\right)+\vec{v}\left(t_2\right)\right]$
(b) $\vec{v}_{ avg }=\left[\vec{r}\left(t_2\right)-\vec{r}\left(t_1\right)\right] /\left(t_2-t_1\right)$
(c) $\vec{v}(t)=\vec{v}(0)+\vec{a} t$
(d) $\vec{r}( t )=\vec{r}(0)+\vec{v}(0) t+(1 / 2) \vec{a} t^2$
(e) $\vec{a}_{\text {avg }}=\left[\vec{v}\left(t_2\right)-\vec{v}\left(t_1\right)\right] /\left(t_2-t_1\right)$
Here, 'average' means the average values of physical quantities related to the time interval $t_2$ and $t_1$.
Pick out the two scalar quantities in the following list :
Force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, relative velocity.
Force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, relative velocity.
State, for each of the following physical quantities, if it is a scalar or a vector : volume, mass, speed, acceleration, density, number of moles, velocity, angular frequency, displacement, angular velocity.
A ball is thrown in horizontal direction from the top of a tower and another ball is dropped from the top of same tower. What will be the time difference between both the balls to reach the earth?
Three girls skating on a circular ice ground of radius 200 m start from a point P on the edge of the ground and reach a point Q diametrically opposite to P following different paths as shown in Fig. What is the magnitude of the displacement vector for each? For which girl is this equal to the actual length of path skate?
Read each statement below carefully and state. with reasons, if it is true or false :
(a) The net acceleration of a particle in circular motion is always along the radius of the circle towards the centre.
(b) The velocity vector of a particle at a point is always along the tangent to the path of the particle at that point.
(c) The acceleration vector of a particle in uniform circular motion averaged over one cycle is a null vector.
(a) The net acceleration of a particle in circular motion is always along the radius of the circle towards the centre.
(b) The velocity vector of a particle at a point is always along the tangent to the path of the particle at that point.
(c) The acceleration vector of a particle in uniform circular motion averaged over one cycle is a null vector.
Explain the difference between two- dimensional and three-dimensional motion by giving examples.
A ball is thrown with a velocity of $15 ms^{-1}$ at angle $45^{\circ}$ with the horizontal. What is the range of ball? What is the time of flight for the ball to return to same plane from the point of throwing?
View full solution →A 0.1 kg stone tied to a thread of 1 m long and moves in a horizontal circular path at a speed of 2 rotations per second. Calculate the tension on the thread.
A cyclist starts from the centre O of a circular park of radius 1 km, reaches the edge P of the park, then cycles along the circumference, and returns to the centre along QO as shown in Fig. If the round trip takes 10 min, what is the (a) net displacement (b) average velocity, and (c) average speed of the cyclist?
Read each statement below carefully and state with reason, if it is true or false :
(a) The magnitude of a vector is always a scalar,
(b) each component of a vector is always a scalar,
(c) the total path length is always equal to the magnitude of the displacement vector of a particle.
(d) the average speed of a particle (defined as total path length divided by the time taken to cover the path) is either greater or equal to the magnitude of average velocity of the particle over the same interval of time, (e) Three vectors not lying in a plane can never add up to give a null vector.
(a) The magnitude of a vector is always a scalar,
(b) each component of a vector is always a scalar,
(c) the total path length is always equal to the magnitude of the displacement vector of a particle.
(d) the average speed of a particle (defined as total path length divided by the time taken to cover the path) is either greater or equal to the magnitude of average velocity of the particle over the same interval of time, (e) Three vectors not lying in a plane can never add up to give a null vector.
State with reasons, whether the following algebraic operations with scalar and vector physical quantities are meaningful :
(a) adding any two scalars, (b) adding a scalar to a vector of the same dimensions, (c) multiplying any vector by any scalar, (d) multiplying any two scalars, (e) adding any two vectors, (f) adding a component of a vector to the same vector.
(a) adding any two scalars, (b) adding a scalar to a vector of the same dimensions, (c) multiplying any vector by any scalar, (d) multiplying any two scalars, (e) adding any two vectors, (f) adding a component of a vector to the same vector.
An aircraft is flying at a height of 3400 m above the ground. If the angle subtendent at a ground observation point by the aircraft position 10.0 s a part is 30º, what is the speed of the aircraft?
Read each statement below carefully and state, with reasons and examples, if it is true or false :
A scalar quantity is one that
(a) is conserved in a process
(b) can never take negative values
(c) must be dimensionless
(d) does not vary from one point to another in space
(e) Has the same value for observers with different orientations of axes.
A scalar quantity is one that
(a) is conserved in a process
(b) can never take negative values
(c) must be dimensionless
(d) does not vary from one point to another in space
(e) Has the same value for observers with different orientations of axes.
The position of a particle is given by $\vec{r}=\left(3 \cdot 0 t \hat{i}-2 \cdot 0 t^2 \hat{j}+4 \cdot 0 \hat{k}\right) m$. where $t$ is in seconds and the coefficient have the proper units for $\vec{r}$ to be in meters.
(a) Find the $\vec{v}$ and $\vec{a}$ of the particle.
(b) What is the magnitude and direction of velocity of the particle at $t=2 s$ ?
View full solution →(a) Find the $\vec{v}$ and $\vec{a}$ of the particle.
(b) What is the magnitude and direction of velocity of the particle at $t=2 s$ ?
A cricketer can throw a ball to a maximum horizontal distance of 100 m. How much high above the ground can the cricketer throw the same ball?
The ceiling of a long hall is 25 m high. What is the maximum horizontal distance that a ball thrown with a speed of $4 0 ms ^{-1}$ can go without hitting the ceiling of the hall?
View full solution →| Column - A | Column - B |
| 1. Position vector of a particle located at point $P$ is $\vec{r}=x \hat{i}+y \hat{j}+z \hat{k}$ the resultant of this $|\vec{r}|=$ | (A) $45^{\circ}$ |
| 2. A vector can be expressed as the product of its magnitude and unit vectorthen $\vec{A}=$ | (B) $\sqrt{x^2+y^2+z^2}$ |
| 3. When $\vec{P}$ and $\vec{Q}$ are in opposite directions then magnitude of $\vec{R} \ldots$. | (C) 1 |
| 4. The sum of squares of all three direction cosines of a vector is always, | (D) $\hat{n}|\overrightarrow{A}|$ |
| 5. The value of $\theta$ for maximum range in $R =\frac{u^2 \sin 2 \theta}{g}$ should be | (E) Minimum |
| Column - A | Column - B |
| 1. The value of centripetal acceleration | (A) $|\overrightarrow{ A }|=$ |
| 2. $\overrightarrow{A}=A_x \hat{i}+A_y \hat{j}+A_z \hat{k}$ the magnitude of $|\overrightarrow{ A }|$ will be : | (B) $H _{\max }=\frac{1}{4} R _{\max }$ |
| 3. Instantaneous acceleration $\vec{a}=$ | (C) Tangential |
| 4. What is the relationship between maximum height and maximum range. | (D) $\frac{d v}{d t}$ |
| 5. The velocity vector is always in the path of motion | (E) $\frac{ V ^2}{ R }$ |
Given $\vec{a}+\vec{b}+\vec{c}+\vec{d}=0$, which of the following statements are correct :
(a) $\vec{a}, \vec{b}, \vec{c}$ and $\vec{d}$ must each be a null vector.
(b) The magnitude of $(\vec{a}+\vec{c})$ equal the magnitude of $(\vec{b}+\vec{d})$.
(c) The magnitude of $\vec{a}$ can never be greater than the sum of magnitudes of $\vec{b}, \vec{c}$ and $\vec{d}$.
(d) $\vec{b}+\vec{c}$ must lie in the plane of $\vec{a}$ and $\vec{d}$ if $\vec{a}$ are not collinear, and in the line of $\vec{a}$ and $\vec{d}$, if they are collinear?
View full solution →(a) $\vec{a}, \vec{b}, \vec{c}$ and $\vec{d}$ must each be a null vector.
(b) The magnitude of $(\vec{a}+\vec{c})$ equal the magnitude of $(\vec{b}+\vec{d})$.
(c) The magnitude of $\vec{a}$ can never be greater than the sum of magnitudes of $\vec{b}, \vec{c}$ and $\vec{d}$.
(d) $\vec{b}+\vec{c}$ must lie in the plane of $\vec{a}$ and $\vec{d}$ if $\vec{a}$ are not collinear, and in the line of $\vec{a}$ and $\vec{d}$, if they are collinear?
Establish the following vector in equalities geometrically or otherwise :
(a) $|\vec{a}+\vec{b}| \leq|\vec{a}|+|\vec{b}|$
(b) $|\vec{a}+\vec{b}| \geq|\vec{a}|-|\vec{b}| \mid$
(c) $|\vec{a}-\vec{b}| \leq|\vec{a}|+|\vec{b}|$
(d) $|\vec{a}-\vec{b}| \geq|\vec{a}|-|\vec{b}| \mid$
When does the equality sign above apply?
View full solution →(a) $|\vec{a}+\vec{b}| \leq|\vec{a}|+|\vec{b}|$
(b) $|\vec{a}+\vec{b}| \geq|\vec{a}|-|\vec{b}| \mid$
(c) $|\vec{a}-\vec{b}| \leq|\vec{a}|+|\vec{b}|$
(d) $|\vec{a}-\vec{b}| \geq|\vec{a}|-|\vec{b}| \mid$
When does the equality sign above apply?
$\hat{i}$ and $\hat{j}$ are unit vectors along $x$ and $y$ axis respectively. What is the magnitude and direction of the vectors $\hat{i}+\hat{j}$ and $\hat{i}-\hat{j}$ ? What are the component of a vector $\overrightarrow{ A }=2 \hat{ i }+3 \hat{ j }$ along the direction of $\hat{i}+\hat{j}$ and $\hat{i}-\hat{j}$ ? (You can use the graphical method).
View full solution →A particle starts from the origin at t = 0 with a velocity of $10 \cdot 0 \hat{ j } m / s$ and moves in the X-Y planes with a constant acceleration of $(8 \cdot 2 \hat{i}+2 \cdot 0 \hat{j}) ms ^{-2}$.
(a) At what time is the $x$-coordinate of the particle 16 m? What is the y -coordinate of the particle at that time?
(b) What is the speed of the particle at that time?
View full solution →(a) At what time is the $x$-coordinate of the particle 16 m? What is the y -coordinate of the particle at that time?
(b) What is the speed of the particle at that time?
On an open ground, a motorist follows a track that turns to his left by an angle of 60º after every 500 m. Starting from a given turn specify the displacement of the motorist at the third, sixth and eighth turn. Compare the magnitude of the displacement with the total path length covered by the motorist in each case.
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