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Kinematics-2D

244 Questions Start Advance Test
All Exams Allen Advance Errorless
Q101 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
An object is projected up the incline at the angle shown in figure with an initial velocity of $30 \, ms^{-1}$ . The distance x up the incline at which the object lands is
A.
$600\mathrm{m}$
B.
$104\mathrm{m}$
C.
$60\mathrm{m}$
D.
$208\mathrm{m}$
Q102 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A very broad elevator is going up vertically with a constant acceleration of $2 \, ms^{-2}$ . At the instant when its velocity is $4 \, ms^{-1}$ a ball is projected from the floor of the lift with a speed of $4 \, ms^{-1}$ relative to the floor at an elevation of $30^\circ$ . The time taken by the ball to return the floor is $(g = 10 \, \text{ms}^{-2})$
A.
1 s
B.
$\frac{1}{2} \, s$
C.
$\frac{1}{3} \, s$
D.
$\frac{1}{4} \, s$
Q103 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
In PROBLEM 86, range of the ball over the floor of the lift is
A.
2 m
B.
$\frac{2}{\sqrt{3}}$ m
C.
$\sqrt{3}$ m
D.
$2\sqrt{3}$ m
Q104 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
An aircraft moving with a speed of $1000 \, kmh^{-1}$ is at a height of $6000 \, m$ , just overhead of an anti-aircraft gun. If the muzzle velocity is $540 \, ms^{-1}$ , the firing angle $\theta$ should be
A.
$73^{\circ}$
B.
$30^{\circ}$
C.
$59^{\circ}$
D.
$45^{\circ}$
Q105 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A particle moves in the $x$ - $y$ plane with velocity $v_x = 8t - 2$ and $v_y = 2$ . If it passes through the point (14, 4) m at $t = 2$ s, the equation of the path is
A.
$x = y^2 - y + 2$
B.
$x = y + 2$
C.
$x = y^2 + 2$
D.
$x = y^2 + y - 2$
Q106 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A rod of length $l$ leans by its upper end against a smooth vertical wall, while its other end leans against the floor. The end that leans against the wall moves uniformly downward with velocity $v_{0}$ . Then
A.
the other end also moves uniformly
B.
the speed of other end goes on decreasing
C.
the speed of other end goes on increasing
D.
the speed of other end first decreases and then increases
Q107 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A particle is projected from the ground with an initial velocity of $30 \, ms^{-1}$ at an angle of $60^\circ$ with horizontal. The magnitude of change in velocity in 2 s is $(g = 10 \, \text{ms}^{-2})$
A.
$5 \, ms^{-1}$
B.
$10 \, ms^{-1}$
C.
$20 \, ms^{-1}$
D.
$40 \, ms^{-1}$
Q108 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A boy throws a ball with a velocity u at an angle $\alpha$ with the vertical. At the same instant he starts running with uniform velocity to catch the ball before it hits the ground. To achieve this, he should run with a velocity of
A.
$u \cos \alpha$
B.
$u \sin \alpha$
C.
$u \tan \alpha$
D.
$\sqrt{u^{2} \tan \alpha}$
Q109 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A projectile is thrown with an initial velocity of $\left(a\hat{i} + b\hat{j}\right)\mathrm{ms}^{-1}$ . If the range of the projectile is twice the maximum height reached by it, then
A.
$a = 2b$
B.
$b = a$
C.
$b = 2a$
D.
$b = 4a$
Q110 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
Time taken by the projectile to reach from $A$ to $B$ is $t$ . Then the distance $AB$ is equal to
A.
$\frac{ut}{\sqrt{3}}$
B.
$\frac{\sqrt{3}ut}{2}$
C.
$\sqrt{3} ut$
D.
$2ut$
Q111 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A stone is projected from a horizontal plane. It attains maximum height H and strikes a stationary smooth wall and falls on the ground vertically below the maximum height. Assume the collision to be elastic, the height of the point on the wall where stone will strike is
A.
$\frac{H}{2}$
B.
$\frac{H}{4}$
C.
$\frac{3H}{4}$
D.
$\frac{H}{3}$
Q112 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A circular disc of radius $r = 5 \, \text{m}$ is rotating in horizontal plane about $y$ -axis. $Y$ -axis is vertical axis passing through the centre of disc and $x-z$ is the horizontal plane at ground. The height of disc above ground is $h = 5 \, \text{m}$ . Small particles are ejecting from disc in horizontal direction with speed $12 \, \text{ms}^{-1}$ from the circumference of disc then the distance of these particles from origin when they hits the $x-z$ plane is
A.
$12 \, \text{m}$
B.
$13 \, \text{m}$
C.
$5 \, \text{m}$
D.
$6 \, \text{m}$
Q113 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
It was calculated that a shell when fired from a gun with a certain velocity and at an angle of elevation $\frac{5\pi}{36}$ radians should strike a given target. In actual practice it was found that a hill just prevented in the trajectory. At what angle of elevation should the gun be fired to hit the target.
A.
$\frac{5\pi}{36}$ radians
B.
$\frac{11\pi}{36}$ radians
C.
$\frac{7\pi}{36}$ radians
D.
$\frac{13\pi}{36}$ radians
Q114 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A body is thrown with speed of $30 \, ms^{-1}$ at angle $30^{\circ}$ with horizontal from a perfectly inelastic horizontal floor. The time after which it is moving perpendicular to its initial direction of motion is
A.
6 s
B.
3 s
C.
1.5 s
D.
never
Q115 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A body is thrown from a point with speed $50 \, ms^{-1}$ at an angle $37^{\circ}$ with horizontal. When it has moved a horizontal distance of 80 m then its distance from point of projection is
A.
40 m
B.
$40\sqrt{2}$ m
C.
$40\sqrt{5}$ m
D.
None of these
Q116 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A ball is thrown from ground level so as to just clear a wall 4 meters high at a distance of 4 meters and falls at a distance of 14 meters from the wall, then the magnitude of the velocity of the ball is
A.
$\sqrt{281}$ ms $^{-1}$
B.
$\sqrt{812}$ ms $^{-1}$
C.
$\sqrt{182}$ ms $^{-1}$
D.
$\sqrt{128}$ ms $^{-1}$
Q117 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
An object is thrown at an angle $\alpha$ to the horizontal $(0^{\circ} < \alpha < 90^{\circ})$ with a velocity. Then during ascent (ignoring air drag) the acceleration
A.
with which the object moves is $\vec{g}$ , at all points.
B.
tangential to the path decreases.
C.
normal to the path increases, becoming equal to $g$ at the highest point.
D.
All of these
Q118 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A projectile is thrown with a velocity of $20 \, ms^{-1}$ , at an angle of $60^\circ$ with the horizontal. After how much time the velocity vector will make an angle of $45^\circ$ with the horizontal? (Take $g = 10 \, ms^{-2}$ )
A.
$\sqrt{3} \, s$
B.
$\frac{1}{\sqrt{3}} \, s$
C.
$(\sqrt{3} + 1) \, s$
D.
$(\sqrt{3} - 1) \, s$
Q119 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A golfer standing on level ground hits a ball with a velocity of $u = 52 \, ms^{-1}$ at an angle $\theta$ above the horizontal. If $\tan\theta = \frac{5}{12}$ , then the time for which the ball is at least 15 m above the ground (i.e. between A and B) will be (take $g = 10 \, ms^{-2}$ )
A.
1 s
B.
2 s
C.
3 s
D.
4 s
Q120 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
Which of the following ideas is helpful in understanding projectile motion?
A.
$v_{x}^{2} + v_{y}^{2} = constant$
B.
Acceleration is +g when the object is rising and -g when falling
C.
In the absence of friction the trajectory will depend on the object's mass as well as its initial velocity and launch angle
D.
The horizontal motion is independent of the vertical motion
Q121 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A ball is projected upwards from the top of the tower with a velocity $50 \, ms^{-1}$ making an angle $30^{\circ}$ with the horizontal. The height of tower is 70 m. After how many seconds the ball will strike the ground?
A.
3 s
B.
5 s
C.
7 s
D.
9 s
Q122 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
The equation of projectile is $y = \sqrt{3}x - \frac{g}{2}x^{2}$ . The angle of projection and initial velocity is
A.
$30^{\circ}$ , $4\ ms^{-1}$
B.
$60^{\circ}$ , $2\ ms^{-1}$
C.
$60^{\circ}$ , $4\ ms^{-1}$
D.
$90^{\circ}$ , $4\ ms^{-1}$
Q123 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A projectile is fired at an angle of $30^{\circ}$ to the horizontal such that the vertical component of its initial velocity is $80~\mathrm{ms}^{-1}$ . Its time of flight is $T$ . Its velocity at $t = \frac{T}{4}$ has a magnitude of nearly
A.
$200~\mathrm{ms}^{-1}$
B.
$300~\mathrm{ms}^{-1}$
C.
$140~\mathrm{ms}^{-1}$
D.
$100~\mathrm{ms}^{-1}$
Q124 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A particle is projected from a point $A$ with velocity $u\sqrt{2}$ at an angle of $45^{\circ}$ with horizontal as shown in figure. It strikes the plane $BC$ at right angles. The velocity of the particle at the time of collision is:
A.
$\frac{\sqrt{3}u}{2}$
B.
$\frac{u}{2}$
C.
$\frac{2u}{\sqrt{3}}$
D.
$u$
Q125 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
Consider a boy on a trolley who throws a ball with speed $20 \, ms^{-1}$ at an angle $37^{\circ}$ with respect to trolley in direction of motion of trolley which moves horizontally with speed $10 \, ms^{-1}$ then what will be maximum distance travelled by ball parallel to road
A.
20.2 m
B.
12 m
C.
31.2 m
D.
62.4 m