Motion in plane practice · Mixed difficulty

A: Two row boats moving parallel to each other and nearby, are attracted towards each other
R: Increase of velocity of fluid flow decrease the pressure

Assertion: Three given concurrent forces may be in equilibrium which is $200 \mathrm{~N} ; 300 \mathrm{~N}$ and 500 $\mathrm{N}$

Reason: Three forces are concurrent and their summation or net force acting on a point is zero when $500 \mathrm{~N}$ acts in one direction and both $200 \mathrm{~N}$ and $300 \mathrm{~N}$ act in the opposite direction.

Two bodies are thrown from the same point with the same velocity of projection, angles of projection $30^\circ$ and $60^\circ .$ If ${R_1}$ and ${R_2}$ are the ranges and ${h_1}$ and ${h_2}$ are maximum heights respectively then

Given $\vec{A}+\vec{B}+\vec{C}+\vec{D}=\overrightarrow{0}$, which of the following statements is not correct?

The maximum and minimum magnitude of the resultant of two given vectors are 17 units and 7 unit respectively. If these two vectors are at right angles to each other, the magnitude of their resultant is

Two particles are projected simultaneously in the same vertical plane, from the same point, both with different speeds and at different angles with horizontal. The path followed by one, as seed by the other, is

For a projectile if $\alpha$ is the angle of projection, $R$ is the range, $h$ is the maximum height, $T$ is the time of flight then

Two shells are fired from a cannon with same speed at angle $\alpha$ and $\beta$ respectively with the horizontal. The time interval between the shots is T. They collide in mid-air after time ' $t$ ' from the first shot. Which of the following conditions must be satisfied?

A swimmer wishes to cross a $800 \mathrm{~m}$ river flowing at $4 \mathrm{~km} / \mathrm{h}$. His speed with respect to water is $3 \mathrm{~km} / \mathrm{h}$. The shortest possible time to cross the river is

Let two non-collinear vectors $\mathbf{a}$ and $\mathbf{b}$ inclined at an angle $\frac{2 \pi}{3}$ be such that $|\mathbf{a}|=3$ and $|\mathbf{b}|=2$. If a point $P$ moves so that at any time $t$ its position vector $\mathbf{O P}$ (where $O$ is the origin) is given as $\mathrm{OP}=\left(t+\frac{1}{t}\right) \mathbf{a}+\left(t-\frac{1}{t}\right) \mathbf{b}$, then least distance of $P$ from the origin is

Which of the following statement(s) is/are correct?

Consider the following statements and select the correct statements from the following.
I. Addition and subtraction of scalars make sense only for quantities with same units
II. Multiplication and division of scalars with different units is possible
III. Addition, subtraction, multiplication and division of scalars with same unit is possible

If a,b and $\mathbf{c}$ are three non-coplanar uni-modular vectors, each inclined with other at an angle $30^{\circ}$, then volume of tetrahedron whose edges are $\mathbf{a}, \mathbf{b}$ and $\mathbf{c}$ is

Pressure is a scalar quantity because

An aeroplane moving horizontally at a speed of $200\mathrm{\;m}{\mathrm{s}^{ - 1}}$ and at a height of $8 \times {10^3}\mathrm{m}$ is to drop a bomb on a target. At what horizontal distance from the target should the bomb be released? (Take $\mathrm{g} = 10\mathrm{\;m}{\mathrm{s}^{ - 2}}$)

A body is under the action of two mutually perpendicular forces of 3 N and 4 N. The resultant force acting on the body is

A body when projected vertically up, covers a total distance $s$, during its time of flight. If we neglect gravity then how much distance the particle will travel during the same time. Will it fall back?

The angle between two vectors $A$ and $B$ is $\theta$. Vector $R$ is the resultant of the two vectors. If $R$ makes an $\frac{\theta}{2}$ with $A$, then

The trajectory of a projectile in a vertical plane is $y = \alpha x - \beta {x^2}$, where $\alpha$ and $\beta$ are constants $x$ and $y$ are respectively the horizontal and vertical distances of the projectile from the point of projection. The angle of projection $\theta$ and the maximum height attained $H$ are respectively given by

The position of particle is given by $\vec{r}=2 t^2 \hat{i}+3 t \hat{j}+4 \hat{k}$ where $t$ is in second and the coefficients have proper units for $\vec{r}$ to be in metre. The $\vec{a}(t)$ of the particle at $t=1 \mathrm{~sec}$ is:

A boat which has a speed of 5 km/hr in still water crosses a river of width 1 km along the shortest possible path in 15 minutes. The velocity of the river water (in km/hr) is

Select the incorrect statement(s) from the following.
I. In projectile motion, the range depends on the mass. It is greater for heavier object
II. In projectile motion, the range is independent of the angle of projection.

A person can throw a ball upto a maximum range of 100 m. How high above the ground he can throw the same ball?

Statement-I: Two particles of different mass, projected with same velocity at same angles. The maximum height attained by both the particle will be same.
Statement-II: The maximum height of projectile is independent of particle mass.

If ${A}=\hat{{i}}+2 \hat{{k}}$ and ${B}=\hat{{j}}-\hat{{k}}$, then, ${A} \times {B}$ is equal to

Statement-I: The value of $\hat{\mathrm{i}}(\hat{\mathrm{j}} \times \hat{\mathrm{k}})+\hat{\mathrm{j}}(\hat{\mathrm{k}} \times \hat{\mathrm{i}})+\hat{\mathrm{k}} \cdot(\hat{\mathrm{i}} \times \hat{\mathrm{j}})$ is equal to 3
Statement-II: If $\hat{a}, \hat{b}, \hat{c}$ are mutually perpendicular unit vectors, then $[\hat{a}, \hat{b}, \hat{c}]=1$

Assertion: A physical quantity can be a vector, if magnitude as well as direction is associated with it.
Reason: A physical quantity can be a scalar quantity, if it is associated with magnitude only.

Assertion: Two vectors $\vec{A}$ and $\vec{B}$ are said to be equal if they have the same magnitude and direction.
Reason: Addition and subtraction of scalars is possible only for quantities having same units.

The angle between the two vectors $- 2\hat i + 3\hat j - \hat k$ and $\hat i + 2\hat j + 4\hat k$ is

If ${A} \cdot {B}=0$ and ${A} \times {B}=1$, then ${A}$ and ${B}$ are