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Kinematics-2D

212 Questions Start Errorless Test
All Exams Allen Advance Errorless
JEE (Main) Jan. 2019 Q76 Errorless 5. Critical Thinking MCQ
A passenger train of length 60m travels at a speed of 80 km/hr. Another freight train of length 120m travels at a speed of 30 km/hr. The ratio of times taken by the passenger train to completely cross the freight train when: (i) they are moving in the same direction, and (ii) in the opposite directions is
A.
$\frac{5}{2}$
B.
$\frac{25}{11}$
C.
$\frac{3}{2}$
D.
$\frac{11}{5}$
JEE (Main) April 2019 Q77 Errorless 5. Critical Thinking MCQ
A plane is inclined at an angle $\alpha = 30^{\circ}$ with a respect to the horizontal. A particle is projected with a speed $u = 2ms^{-1}$ from the base of the plane, making an angle $\theta = 15^{\circ}$ with respect to the plane as shown in the figure. The distance from the base, at which the particle hits the plane is close to (Take $g = 10ms^{-2}$ )
A.
$14cm$
B.
$20cm$
C.
$18cm$
D.
$26cm$
JEE (Main) April 2019 Q78 Errorless 5. Critical Thinking MCQ
The trajectory of a projectile near the surface of the earth is given as $y = 2x - 9x^2$ . If it were launched at an angle $\theta_0$ with speed $v_0$ then ( $g = 10ms^{-2}$ )
A.
$\theta_0 = \cos^{-1}\left(\frac{1}{\sqrt{5}}\right)$ and $v_0 = \frac{5}{3}ms^{-1}$
B.
$\theta_0 = \sin^{-1}\left(\frac{1}{\sqrt{5}}\right)$ and $v_0 = \frac{5}{3}ms^{-1}$
C.
$\theta_0 = \sin^{-1}\left(\frac{2}{\sqrt{5}}\right)$ and $v_0 = \frac{3}{5}ms^{-1}$
D.
$\theta_0 = \cos^{-1}\left(\frac{2}{\sqrt{5}}\right)$ and $v_0 = \frac{3}{5}ms^{-1}$
JEE (Main) April 2019 Q79 Errorless 5. Critical Thinking MCQ
A shell is fired from a fixed artillery gun with an initial speed $u$ such that it hits the target on the ground at a distance $R$ from it. If $t_1$ and $t_2$ are the values of the time taken by it to hit the target in two possible ways, the product $t_1t_2$ is
A.
$R / g$
B.
$R / 4g$
C.
$2R / g$
D.
$R / 2g$
JEE (Main) April 2019 Q80 Errorless 5. Critical Thinking MCQ
A smooth wire of length $2\pi r$ is bent into a circle and kept in a vertical plane. A bead can slide smoothly on the wire. When the circle is rotating with angular speed $\omega$ about the vertical diameter AB, as shown in figure, the bead is at rest with respect to the circular ring at position P as shown. Then the value of $\omega^{2}$ is equal to
A.
$\left(g\sqrt{3}\right) / r$
B.
$\frac{\sqrt{3}g}{2r}$
C.
$2g / r$
D.
$2g / (r\sqrt{3})$
JEE (Main) April 2019 Q81 Errorless 5. Critical Thinking MCQ
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
A.
$R^2 = 2h_1h_2$
B.
$R^2 = 16h_1h_2$
C.
$R^2 = 4h_1h_2$
D.
$R^2 = h_1h_2$
JEE (Advanced) 2019 Q82 Errorless 7. JEE Section Numerical
A ball is thrown from ground at an angle $\theta$ with horizontal and with an initial speed $u_0$ . For the resulting projectile motion, the magnitude of average velocity of the ball up to the point when it hits the ground for the first time is $V_1$ . After hitting the ground, ball rebounds at the same angle $\theta$ but with a reduced speed of $u_0 / \alpha$ . Its motion continues for a long time as shown in figure. If the magnitude of average velocity of the ball for entire duration of motion is 0.8 $V_1$ , the value of $\alpha$ is ____
JEE (Advanced) 2018 Q83 Errorless 7. JEE Section Numerical
A ball is projected from the ground at an angle of $45^{\circ}$ with the horizontal surface. It reaches a maximum height of 120 m and returns to the ground. Upon hitting the ground for the first time, it loses half of its kinetic energy. Immediately after the bounce, the velocity of the ball makes an angle of $30^{\circ}$ with the horizontal surface. The maximum height it reaches after the bounce, in metres, is
JEE (Advanced) 2017 Q84 Errorless 5. Critical Thinking MCQ
Consider an expanding sphere of instantaneous radius R whose total mass remains constant. The expansion is such that the instantaneous density $\rho$ remains uniform throughout the volume. The rate of fractional change in density $\left(\frac{1}{\rho}\frac{d\rho}{dt}\right)$ is constant. The velocity v of any point on the surface of the expanding sphere is proportional to
A.
$R^{3}$
B.
R
C.
$R^{2/3}$
D.
$\frac{1}{R}$
NEET (Phase-I) 2016 Q85 Errorless 2. Non-uniform Circular Motion MCQ
A particle of mass 10 g moves along a circle of radius 6.4 cm with a constant tangential acceleration. What is the magnitude of this acceleration if the kinetic energy of the particle becomes equal to $8 \times 10^{-4} J$ by the end of the second revolution after the beginning of the motion
A.
$0.1 m/s^{2}$
B.
$0.15 m/s^{2}$
C.
$0.18 m/s^{2}$
D.
$0.2 m/s^{2}$
NEET (Phase-II) 2016 Q86 Errorless 2. Non-uniform Circular Motion MCQ
In the given figure, $a = 15m / s^2$ represents the total acceleration of a particle moving in the clockwise direction in a circle of radius $R = 2.5m$ at a given instant of time. The speed of the particle is
A.
6.2 m/s
B.
4.5 m/s
C.
5.0 m/s
D.
5.7 m/s
JEE (Main) 2016 Q87 Errorless 2. Non-uniform Circular Motion MSQ
A particle of mass $m$ is moving along the side of square of side 'a' with a uniform speed $v$ in the $x-y$ plane as shown in the figure Which of the following statements is false for the angular momentum $\vec{L}$ about the origin
A.
$\vec{L} = mv\left[\frac{R}{\sqrt{2}} - a\right]\hat{k}$ when the particle is moving from $C$ to $D$
B.
$\vec{L}=mv\left[\frac{R}{\sqrt{2}}+a\right]\hat{k}$ when the particle is moving from B to C
C.
$\vec{L}=\frac{mv}{\sqrt{2}}R\hat{k}$ when the particle is moving from D to A
D.
$\vec{L}=-\frac{mv}{\sqrt{2}}R\hat{k}$ when the particle is moving from A to B
NEET (Phase-I) 2016 Q88 Errorless 2. Non-uniform Circular Motion MCQ
What is the minimum velocity with which a body of mass m must enter a vertical loop of radius R so that it can complete the loop
A.
$\sqrt{gR}$
B.
$\sqrt{2gR}$
C.
$\sqrt{3gR}$
D.
$\sqrt{5gR}$
NEET (Phase-I) 2016 Q89 Errorless 2. Non-uniform Circular Motion MCQ
A uniform circular disc of radius 50 cm at rest is free to turn about an axis which is perpendicular to its plans and passes through its centre. It is subjected to a torque which produces a constant angular acceleration of 2.0 rad s $^{-2}$ . Its net acceleration in ms $^{-2}$ at the end of 2.0 s is approximately
A.
8.0
B.
7.0
C.
6.0
D.
3.0
MH CET 2015 Q90 Errorless 1. Uniform Circular Motion MCQ
The difference between angular speed of minute hand and second hand of a clock is
A.
$\frac{59\pi}{900}rad/s$
B.
$\frac{59\pi}{1800}rad/s$
C.
$\frac{59\pi}{2400}rad/s$
D.
$\frac{59\pi}{3600}rad/s$
WB-JEE 2015 Q91 Errorless 2. Non-uniform Circular Motion MCQ
A simple pendulum of length L swings in a vertical plane. The tension of the string when it makes an angle $\theta$ with the vertical and the bob of mass m moves with a speed v is (g is the gravitational acceleration)
A.
$mv^{2}/L$
B.
$mg\cos\theta + mv^{2}/L$
C.
$mg\cos\theta - mv^{2}/L$
D.
$mg\cos\theta$
KCET 2015 Q92 Errorless 4. Oblique Projectile Motion MCQ
A particle is projected with a velocity v so that its horizontal range is twice the greatest height attained. The horizontal range is
A.
$\frac{2v^{2}}{3g}$
B.
$\frac{v^{2}}{2g}$
C.
$\frac{v^{2}}{g}$
D.
$\frac{4v^{2}}{5g}$
KCET 2015 Q93 Errorless 5. Critical Thinking MCQ
The ratio of angular speed of a second-hand to the hour-hand of a watch is
A.
60:1
B.
72:1
C.
720:1
D.
3600:1
JEE (Main) 2015 Q94 Errorless 6. Graphical Questions MCQ
Two stones are thrown up simultaneously from the edge of a cliff 240 m high with initial speed of 10 m/s and 40 m/s respectively. Which of the following graph best represents the time variation of relative position of the second stone with respect to the first (Assume stones do not rebound after hitting the ground and neglect air resistance, take $g=10m/s^{2}$ ). (The figures are schematic and not drawn to scale)
A.
B.
C.
D.
JEE (Main) 2013 Q95 Errorless 4. Oblique Projectile Motion MCQ
A projectile is given an initial velocity of $(\hat{i} + 2\hat{j})$ m/s, where $\hat{i}$ is along the ground and $\hat{j}$ is along the vertical. If $g = 10m/s^{2}$ , the equation of its trajectory is
A.
$y = x - 5x^{2}$
B.
$y = 2x - 5x^{2}$
C.
$4y = 2x - 5x^{2}$
D.
$4y = 2x - 25x^{2}$
JEE (Advanced) 2013 Q96 Errorless 4. Oblique Projectile Motion MCQ
A particle of mass m is projected from the ground with an initial speed $u_{0}$ at an angle $\alpha$ with the horizontal. At the highest point of its trajectory, it makes a completely inelastic collision with another identical particle, which was thrown vertically upward from the ground with the same initial speed $u_{0}$ . The angle that the composite system makes with the horizontal immediately after the collision is
A.
$\frac{\pi}{4}$
B.
$\frac{\pi}{4} + \alpha$
C.
$\frac{\pi}{4} - \alpha$
D.
$\frac{\pi}{2}$
WB-JEE 2013 Q97 Errorless 4. Oblique Projectile Motion MCQ
A body is projected from the ground with a velocity $\vec{v} = (3\hat{i} + 10\hat{j})ms^{-1}$ . The maximum height attained and the range of the body respectively are (given $g = 10ms^{-2}$ )
A.
$5m$ and $6m$
B.
$3m$ and $10m$
C.
$6m$ and $5m$
D.
$3m$ and $5m$
NEET 2013 Q98 Errorless 4. Oblique Projectile Motion MCQ
The velocity of a projectile at the initial point A is $(2\hat{i} + 3\hat{j})m/s$ . It's velocity (in m/s) at point B is
A.
$2\hat{i} + 3\hat{j}$
B.
$-2\hat{i} - 3\hat{j}$
C.
$-2\hat{i} + 3\hat{j}$
D.
$2\hat{i} - 3\hat{j}$
AIEEE 2012 Q99 Errorless 1. Uniform Circular Motion MCQ
Two cars of masses $m_{1}$ and $m_{2}$ are moving in circles of radii $r_{1}$ and $r_{2}$ respectively. Their speeds are such that they make complete circles in the same time t. The ratio of their centripetal acceleration is
A.
$m_{1}r_{1}:m_{2}r_{2}$
B.
$m_{1}:m_{2}$
C.
$r_{1}:r_{2}$
D.
1:1
Odisha JEE 2012 Q100 Errorless 1. Uniform Circular Motion MCQ
A body moves in a circle covers equal distance in equal intervals of time. Which of the following remains constant
A.
Velocity
B.
Acceleration
C.
Speed
D.
Displacement