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Kinematics-2D

384 Questions Start Objective Test
All Exams Allen Objective Errorless
JEE (Main) 2021 Q26 Errorless Critical Thinking MCQ
A player kicks a football with an initial speed of $25ms^{-1}$ at an angle of $45^{\circ}$ from the ground. What are the maximum height and the time taken by the football to reach at the highest point during motion (Take $g = 10 ms^{-2}$ )
A.
$h_{max} = 15.625m, T = 1.77s$
B.
$h_{max} = 3.54m, T = 0.125s$
C.
$h_{max} = 10m, T = 2.5s$
D.
$h_{max} = 15.625m, T = 3.54s$
JEE (Main) 2021 Q27 Errorless Critical Thinking MCQ
Particle of mass m is suspended from a ceiling through a string of length L. The particle moves in a horizontal circle of radius r such that $r=\frac{L}{\sqrt{2}}$ . The speed of particle will be
A.
$\sqrt{\frac{rg}{2}}$
B.
$2\sqrt{rg}$
C.
$\sqrt{2rg}$
D.
$\sqrt{rg}$
NEET 2021 Q28 Errorless Critical Thinking MCQ
A particle moving in a circle of radius $R$ with a uniform speed takes a time $T$ to complete one revolution. If this particle were projected with the same speed at an angle ' $\theta'$ to the horizontal, the maximum height attained by it equals 4R. The angle of projection $\theta$ , is then given by
A.
$\theta = \cos^{-1}\left(\frac{\pi^2R}{gT^2}\right)^{1/2}$
B.
$\theta = \sin^{-1}\left(\frac{\pi^2R}{gT^2}\right)^{1/2}$
C.
$\theta = \sin^{-1}\left(\frac{2gT^2}{\pi^2R}\right)^{1/2}$
D.
$\theta = \cos^{-1}\left(\frac{gT^2}{\pi^2R}\right)^{1/2}$
NEET 2021 Q29 Errorless Critical Thinking MCQ
A car starts from rest and accelerates at $5m/s^{2}$ . At t=4s, a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at t=6s (Take $g=10m/s^{2}$ )
A.
20 m/s, 0
B.
$20\sqrt{2}m/s,0$
C.
$20\sqrt{2}m/s,10m/s^{2}$
D.
$20m/s,5m/s^{2}$
JEE (Main) 2020 Q30 Errorless Critical Thinking MCQ
A particle starts from the origin at t=0 with an initial velocity of $3.0\hat{i}$ m/s and moves in the x-y plane with a constant acceleration $(6.0\hat{i}+4.0\hat{j})m/s^{2}$ . The x-coordinate of the particle at the instant when its y-co-ordinate is 32 m is D meters. The value of D is
A.
50
B.
32
C.
60
D.
40
JEE (Main) 2020 Q31 Errorless Critical Thinking MCQ
A Tennis ball is released from a height h and after freely falling on a wooden floor it rebounds and reaches height $\frac{h}{2}$ . The velocity versus height of the ball during its motion may be represented graphically by (graph are drawn schematically and on not to scale)
A.
B.
C.
D.
JEE (Main) 2020 Q32 Errorless Critical Thinking MCQ
A small ball of mass m is thrown upward with velocity u from the ground. The ball experiences a resistive force $mkv^{2}$ where v is it speed. The maximum height attained by the ball is
A.
$\frac{1}{2k}\tan^{-1}\frac{ku^{2}}{g}$
B.
$\frac{1}{k}\ln\left(1+\frac{ku^{2}}{2g}\right)$
C.
$\frac{1}{k}\tan^{-1}\frac{ku^{2}}{2g}$
D.
$\frac{1}{2k}\ln\left(1+\frac{ku^{2}}{g}\right)$
JEE (Main) 2020 Q33 Errorless Critical Thinking MCQ
A clock has a continuously moving second's hand of $0.1m$ length. The average acceleration of the tip of the hand (in units of $ms^{-2}$ ) is of the order of
A.
$10^{-3}$
B.
$10^{-2}$
C.
$10^{-4}$
D.
$10^{-1}$
JEE (Main) 2020 Q34 Errorless Critical Thinking MCQ
A particle moving in the xy plane experiences a velocity dependent force $\vec{F} = k(v_y\hat{i} + v_x\hat{j})$ , where $v_x$ and $v_y$ are the $x$ and $y$ components of its velocity $\vec{v}$ . If $\vec{a}$ is the acceleration of the particle, then which of the following statements is true for the particle
A.
Quantity $\vec{v}.\vec{a}$ is constant in time
B.
Kinetic energy of particle is constant in time
C.
Quantity $\vec{v} \times \vec{a}$ is constant in time
D.
$\vec{F}$ arises due to a magnetic field
NEET 2019 Q35 Objective Collection of questions asked in NEET & various medical entrance exams MCQ
When an object is shot from the bottom of a long smooth inclined plane kept at an angle $60^{\circ}$ with horizontal, it can travel a distance $x_{1}$ along the plane. But when the inclination is decreased to $30^{\circ}$ and the same object is shot with the same velocity, it can travel $x_{2}$ distance. Then, $x_{1}:x_{2}$ will be
A.
$\sqrt{2}:1$
B.
$1:\sqrt{3}$
C.
$1:2\sqrt{3}$
D.
$1:\sqrt{2}$
NEET (Odisha) 2019 Q36 Objective Collection of questions asked in NEET & various medical entrance exams MCQ
Two bullets are fired horizontally and simultaneously towards each other from roof tops of two buildings 100 m apart and of same height of 200 m with the same velocity of $25 \, ms^{-1}$ . When and where will the two bullets collides? (Take, $g = 10 \, ms^{-2}$ )
A.
After 2s at a height of 180 m
B.
After 2s at a height of 20 m
C.
After 4s at a height of 120 m
D.
They will not collide
JEE (Main) 2019 Q37 Errorless Critical Thinking MCQ
The position co-ordinates of a particle moving in a 3-D coordinate system is given by $x = a \cos \omega t$ $y = a \sin \omega t$ and $z = a \omega t$ The speed of the particle is
A.
$a\omega$
B.
$\sqrt{3}a\omega$
C.
$\sqrt{2}a\omega$
D.
$2a\omega$
JEE (Main) 2019 Q38 Errorless Critical Thinking MCQ
Two guns A and B can fire bullets at speeds 1km/s and 2km/s respectively. From a point on a horizontal ground, they are fired in all possible directions. The ratio of maximum areas covered by the bullets fired by the two guns, on the ground is
A.
1:2
B.
1:4
C.
1:8
D.
1:16
JEE (Main) 2019 Q39 Errorless Critical Thinking MCQ
A body is projected at t=0 with a velocity $10ms^{-1}$ at an angle of $60^{\circ}$ with the horizontal. The radius of curvature of its trajectory at t=1s is R. Neglecting air resistance and taking acceleration due to gravity $g=10ms^{-2}$ , the value of R is
A.
2.5 m
B.
10.3 m
C.
2.8 m
D.
5.1 m
JEE (Main) 2019 Q40 Errorless Critical Thinking MCQ
A particle is moving along a circular path with a constant speed of $10ms^{-1}$ . What is the magnitude of the change is velocity of the particle, when it moves through an angle of $60^{\circ}$ around the centre of the circle
A.
Zero
B.
10m/s
C.
$10\sqrt{3}m/s$
D.
$10\sqrt{2}m/s$
JEE (Main) 2019 Q41 Errorless 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) 2019 Q42 Errorless 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.
14 cm
B.
20 cm
C.
18 cm
D.
26 cm
JEE (Main) 2019 Q43 Errorless 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) 2019 Q44 Errorless 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) 2019 Q45 Errorless 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.
$(g\sqrt{3}) / r$
B.
$\frac{\sqrt{3}g}{2r}$
C.
$2g / r$
D.
$2g / (r\sqrt{3})$
JEE (Main) 2019 Q46 Errorless 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.
$R^2 = h_1h_2$
NEET 2019 Q47 Errorless Critical Thinking MCQ
A mass m is attached to a thin wire and whirled in a vertical circle. The wire is most likely to break when
A.
The mass is at the highest point
B.
The wire is horizontal
C.
The mass is at the lowest point
D.
Inclined at an angle $60^{\circ}$ from vertical
NEET 2019 Q48 Errorless Critical Thinking MCQ
Two particles A and B are moving in uniform circular motion in concentric circles of radius $r_{A}$ and $r_{B}$ with speed $v_{A}$ and $v_{B}$ respectively. The time period of rotation is the same. The ratio of angular speed of A to that of B will be
A.
$r_{A}:r_{B}$
B.
$v_{A}:v_{B}$
C.
$r_{B}:r_{A}$
D.
1:1
NEET 2019 Q49 Errorless Critical Thinking MCQ
When an object is shot from the bottom of a long smooth inclined plane kept at an angle $60^{\circ}$ with horizontal, it can travel a distance $x_{1}$ along the plane. But when the inclination is decreased to $30^{\circ}$ and the same object the shot with the same velocity, it can travel $x_{2}$ distance. Then $x_{1}: x_{2}$ will be
A.
$1: \sqrt{2}$
B.
$\sqrt{2}: 1$
C.
$1: \sqrt{3}$
D.
$1: 2\sqrt{3}$
AIIMS 2018 Q50 Objective Collection of questions asked in NEET & various medical entrance exams MCQ
Assertion The maximum height of projectile is always 25% of the maximum range. Reason For maximum range, projectile should be projected at 90°.
A.
If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
B.
If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.
C.
If Assertion is correct but Reason is incorrect.
D.
If Assertion is incorrect but Reason is correct.