List of top Physics Questions on Motion in a plane

Two vectors are given by $\vec{A} = \hat{i} - 2\hat{j} + 3\hat{k}$ and $\vec{B} = 2\hat{i} - 4\hat{j} + 3\hat{k}$. The unit vector along $\vec{A} + \vec{B}$ is

The vertical displacement (y in metre) of a projectile in terms of its horizontal displacement (x in metre) is given by $y=(\sqrt{3}x - 0.2x^2)$. The time of flight of the projectile is (Acceleration due to gravity = 10 ms$^{-2}$)

A ball projected at an angle of 45$^\circ$ with the horizontal crosses two points at equal heights separated by a distance at times 2 s and 8 s respectively. The horizontal distance between the two points is (Acceleration due to gravity = 10 ms$^{-2}$)

If a body projected with a velocity of 19.6 ms⁻¹ reaches a maximum height of 9.8 m, then the range of the projectile is (Neglect air resistance)

A ball is thrown vertically upwards with an initial velocity of $ 20 \, \text{m/s} $. How high will the ball rise? (Take $ g = 10 \, \text{m/s}^2 $)

A person travelling on a straight line moves with a uniform velocity $ v_1 $ for a distance $ x $ and with a uniform velocity $ v_2 $ for the next $ \frac{3x}{2} $ distance. The average velocity in this motion is $ \frac{50}{7} \, \text{m/s} $. If $ v_1 $ is 5 m/s, then $ v_2 $ is ___ m/s.

If two vectors $\vec{A}$ and $\vec{B}$ having equal magnitude $R$ are inclined at an angle $\theta$, then

The resultant of two vectors $ \vec{A} $ and $ \vec{B} $ is perpendicular to $ \vec{A} $ and its magnitude is half that of $ \vec{B} $. The angle between vectors $ \vec{A} $ and $ \vec{B} $ is ________ .

A Particle is projected vertically upward reaches 136 m height. What will be the maximum range for the particle projected with same speed ?

A particle moves in a circular path with uniform speed v. When it turns by 90°, find ratio of $\frac{v}{<\overrightarrow{v}>}$?

Two forces of magnitude A and $\frac{A}{2}$ act perpendicular to each other. The magnitude of the resultant force is equal to:

Two projectiles u₁ and u₂, with speed of 40 m/s and 60 m/s respectively are thrown at a certain angle, u₁ with 30^o and u₂ with 60^o, what is the ratio of range?

The speed of a swimmer is $4 km h ^{-1}$ in still water If the swimmer makes his strokes normal to the flow of river of width $1 km$, he reaches a point $750 m$ down the stream on the opposite bank.The speed of the river water is ___ $km h ^{-1}$

For a periodic motion represented by the equation y = sin ωt + cos ωt, the amplitude of the motion is

A solid sphere is rolling on a horizontal plane without slipping. If the ratio of angular momentum about axis of rotation of the sphere to the total energy of moving sphere is π : 22 then, the value of its angular speed will be ______ rad/s.

If force $\vec F=3\hat i+4\hat j−2\hat k$ acts on a particle having position vector $2\hat i+\hat j+2\hat k$ then, the torque about the origin will be

Two projectile thrown at $30^{\circ}$ and $45^{\circ}$ with the horizontal respectively, reach the maximum height in same time The ratio of their initial velocities is

$\vec A$ is a vector quantity such that
$|\vec A|$ = non-zero constant.
Which of the following expression is true for $\vec A$?

Which of the following relations is true for two unit vector $\hat A$ and $\hat B$ making an angle θ to each other?

Two buses P and Q start from a point at the same time and move in a straight line and their positions are represented by X_P(t) = αt + βt² and X_Q(t) = ft – t². At what time, both the buses have same velocity?

A disc with a flat small bottom beaker placed on it at a distance R from its center is revolving about an axis passing through the center and perpendicular to its plane with an angular velocity ω. The coefficient of static friction between the bottom of the beaker and the surface of the disc is μ. The beaker will revolve with the disc if :

A solid metallic cube having total surface area 24 m² is uniformly heated. If its temperature is increased by 10°C, calculate the increase in volume of the cube.

(Given α = 5.0 × 10^–4 °C^–1).

At time t = 0 a particle starts travelling from a height $7\hat z cm$ in a plane keeping $z$ coordinate constant. At any instant time it's position along the $x$ and $y$ directions are defined as $3t$ and $5t^3$ respectively. At $t = 1s$ acceleration of the particle will be

A bomb is dropped by a fighter plane flying horizontally. To an observer sitting in the plane, the trajectory of the bomb is a :

Two particles are projected from the same point with the same speed $u$ such that they have the same range $R$, but different maximum heights, $h_1$ and $h_2$. Which of the following is correct ?