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Kinematics-2D

212 Questions Start Errorless Test
All Exams Allen Advance Errorless
J & K CET 2012 Q101 Errorless 1. Uniform Circular Motion MCQ
A brick of mass m, tied to a rope, is being whirled in a vertical circle, with a uniform speed. The tension in the rope is
A.
The same throughout
B.
Largest when the brick is at the highest point of the circular path and smallest when it is at the lowest point
C.
Largest when the rope is horizontal and smallest when it is vertical
D.
Largest when the brick is at the lowest point and smallest when it is at the highest point
AMU (Engg.) 2012 Q102 Errorless 2. Non-uniform Circular Motion MCQ
What is approximately the centripetal acceleration (in units of acceleration due to gravity on earth, $g = 10 \, m/s^{2}$ ) of an air-craft flying at a speed of 400 m/s through a circular arc of radius 0.6 km
A.
26.7
B.
16.9
C.
13.5
D.
30.2
CBSE PMT (Pre.) 2012 Q103 Errorless 3. Horizontal Projectile Motion MCQ
The horizontal range and the maximum height of a projectile are equal. The angle of projection of the projectile is
A.
$\theta = \tan^{-1}\left(\frac{1}{4}\right)$
B.
$\theta = \tan^{-1}(4)$
C.
$\theta = \tan^{-1}(2)$
D.
$\theta = 45^{\circ}$
AIEEE 2012 Q104 Errorless 3. Horizontal Projectile Motion MCQ
A boy can throw a stone up to a maximum height of 10m. The maximum horizontal distance that the boy can throw the same stone up to will be
A.
$20\sqrt{2}m$
B.
10m
C.
$10\sqrt{2}m$
D.
20m
IIT JEE 2012 Q105 Errorless 5. Critical Thinking MCQ
Consider a disc rotating in the horizontal plane with a constant angular speed $\omega$ about its centre $O$ . The disc has a shaded region on one side of the diameter and an unshanded region on the other side as shown in the figure. When the disc is in the orientation as shown, two pebbles $P$ and $Q$ are simultaneously projected at an angle towards $R$ . The velocity of projection is in the $y-z$ plane and is same for both pebbles with respect to the disc. Assume that (i) they land back on the disc before the disc has completed $\frac{1}{8}$ rotation. (ii) their range is less than half the disc radius, and (iii) $\omega$ remains constant throughout. Then
A.
P lands in the shaded region and Q in the unshaded region
B.
$P$ lands in the unshaded region and $Q$ in the shaded region
C.
Both $P$ and $Q$ land in the unshaded region
D.
Both $P$ and $Q$ land in the shaded region
IIT-JEE 2012 Q106 Errorless 5. Critical Thinking MCQ
A small mass m is attached to a massless string whose other end is fixed at P as shown in the figure. The mass is undergoing circular motion in the x-y plane with centre at O and constant angular speed $\omega$ . If the angular momentum of the system, calculated about O and P are denoted by $\vec{L}_{O}$ and $\vec{L}_{P}$ respectively, then
A.
$\vec{L}_O$ and $\vec{L}_P$ do not vary with time
B.
$\vec{L}_{O}$ varies with time while $\vec{L}_{P}$ remains constant
C.
$\vec{L}_O$ remains constant while $\vec{L}_P$ varies with time
D.
$\vec{L}_O$ and $\vec{L}_P$ both vary with time
IIT JEE 2012 Q107 Errorless 6. Graphical Questions MCQ
Two identical discs of same radius R are rotating about their axes in opposite directions with the same constant angular speed $\omega$ . The discs are in the same horizontal plane. At time t=0, the points P and Q are facing each other as shown in the figure. The relative speed between the two points P and Q is $V_{r}$ as function of times best represented by
A.
B.
C.
D.
CBSE PMT (Pre.) 2011 Q108 Errorless 1. Uniform Circular Motion MCQ
A particle moves in a circle of radius 5 cm with constant speed and time period $0.2\pi s$ . The acceleration of the particle is
A.
$5m/s^{2}$
B.
$15m/s^{2}$
C.
$25m/s^{2}$
D.
$36m/s^{2}$
CBSE PMT (Mains) 2011 Q109 Errorless 4. Oblique Projectile Motion MCQ
A projectile is fired at an angle of $45^{\circ}$ with the horizontal. Elevation angle of the projectile at its highest point as seen from the point of projection, is
A.
$\tan^{-1}\left(\frac{\sqrt{3}}{2}\right)$
B.
$45^{\circ}$
C.
$60^{\circ}$
D.
$\tan^{-1}\frac{1}{2}$
Kerala PET 2011 Q110 Errorless 4. Oblique Projectile Motion MCQ
A particle crossing the origin of co-ordinates at time t=0, moves in the xy-plane with a constant acceleration a in the y-direction. If its equation of motion is $y=bx^{2}$ (b is a constant), its velocity component in the x-direction is
A.
$\sqrt{\frac{2b}{a}}$
B.
$\sqrt{\frac{a}{2b}}$
C.
$\sqrt{\frac{a}{b}}$
D.
$\sqrt{\frac{b}{a}}$
E.
$\sqrt{ba}$
IIT-JEE 2011 Q111 Errorless 7. JEE Section Numerical
A train is moving along a straight line with a constant acceleration 'a'. A boy standing in the train throws a ball forward with a speed of 10 m/s, at an angle of $60^{\circ}$ to the horizontal. The boy has to move forward by 1.15 m inside the train to catch the ball back at the initial height. The acceleration of the train, in $m/s^{2}$ , is
J & K CET 2010 Q112 Errorless 1. Uniform Circular Motion MCQ
If a car is to travel with a speed v along the frictionless, banked circular track of radius r, the required angle of banking so that the car does skid is
A.
$\theta = \tan^{-1}\left(\frac{v^{2}}{rg}\right)$
B.
$\theta = \tan^{-1}\left(\frac{v}{rg}\right)$
C.
$\theta = \tan^{-1}\left(\frac{r^{2}}{vg}\right)$
D.
$\theta < \tan^{-1}\left(\frac{v^{2}}{rg}\right)$
J & K CET 2010 Q113 Errorless 1. Uniform Circular Motion MCQ
Which one of the following statements is not correct in uniform circular motion
A.
The speed of the particle remains constant
B.
The acceleration always points towards the centre
C.
The angular speed remains constant
D.
The velocity remains constant
DUMET 2010 Q114 Errorless 3. Horizontal Projectile Motion MCQ
A child travelling in a train throws a ball outside with a speed V. According to a child who is standing on the ground, the speed of the ball is
A.
Same as V
B.
Greater than V
C.
Less than V
D.
None of these
CBSE PMT (Mains) 2010 Q115 Errorless 4. Oblique Projectile Motion MCQ
The speed of a projectile at its maximum height is half of its initial speed. The angle of projection is
A.
$60^{\circ}$
B.
$15^{\circ}$
C.
$30^{\circ}$
D.
$45^{\circ}$
AIEEE 2010 Q116 Errorless 4. Oblique Projectile Motion MCQ
A small particle of mass m is projected at an angle $\theta$ with the x-axis with an initial velocity $v_{0}$ in the x-y plane as shown in the figure. At a time $t < \frac{v_{0} \sin \theta}{g}$ , the angular momentum of the particle is where $\hat{i},\hat{j}$ and $\hat{k}$ are unit vectors along x, y and z-axis respectively.
A.
$\frac{1}{2} mgv_0t^2\cos \theta \hat{i}$
B.
$-mgv_0t^2\cos \theta \hat{j}$
C.
$mgv_0t\cos \theta \hat{k}$
D.
$-\frac{1}{2} mgv_0t^2\cos \theta \hat{k}$
J & K CET 2010 Q117 Errorless 4. Oblique Projectile Motion MCQ
An object is projected so that its horizontal range $R$ is maximum. If the maximum height attained by the object is $H$ , then the ratio of $R / H$ is
A.
4
B.
1/4
C.
2
D.
1/2
WB-JEE 2010 Q118 Errorless 4. Oblique Projectile Motion MCQ
A body is projected with a speed $u$ m/s at an angle $\beta$ with the horizontal. The kinetic energy at the highest point is $\frac{3}{4}th$ of the initial kinetic energy. The value of $\beta$ is
A.
$30^{\circ}$
B.
$45^{\circ}$
C.
$60^{\circ}$
D.
$120^{\circ}$
AIEEE 2010; JEE (Main) April 2019 Q119 Errorless 5. Critical Thinking MCQ
A particle is moving with velocity $\vec{v} = K(y\hat{i} + x\hat{j})$ , where $K$ is a constant. The general equation for its path is
A.
$y^{2} = x^{2} + \text{constant}$
B.
$y = x^{2} + \text{constant}$
C.
$y^{2} = x + \text{constant}$
D.
$xy = \text{constant}$
DUMET 2009 Q120 Errorless 1. Uniform Circular Motion MCQ
An object moves at a constant speed along a circular path in a horizontal XY plane, with the centre at the origin. When the object is at $x = -2m$ , its velocity is $-(4m / s)\hat{j}$ . What is the object's acceleration when it is $y = 2m$
A.
$-(8m / s^2)\hat{j}$
B.
$-(8m / s^2)\hat{i}$
C.
$-(4m / s^2)\hat{j}$
D.
$(4m / s^2)\hat{i}$
EAMCET 2009 Q121 Errorless 4. Oblique Projectile Motion MCQ
A body is projected vertically upwards at time t = 0 and it is seen at a height H at instants $t_{1}$ and $t_{2}$ seconds during its flight. The maximum height attained is (g is acceleration due to gravity)
A.
$\frac{g(t_{2}-t_{1})^{2}}{8}$
B.
$\frac{g(t_{1}+t_{2})^{2}}{4}$
C.
$\frac{g(t_{1}+t_{2})^{2}}{8}$
D.
$\frac{g(t_{2}-t_{1})^{2}}{4}$
WB-JEE 2009 Q122 Errorless 4. Oblique Projectile Motion MCQ
A bullet is fired with a velocity $u$ making an angle of $60^{\circ}$ with the horizontal plane. The horizontal component of the velocity of the bullet when it reaches the maximum height is
A.
$u$
B.
0
C.
$\frac{\sqrt{3u}}{2}$
D.
$u / 2$
DUMET 2009 Q123 Errorless 4. Oblique Projectile Motion MCQ
A coastguard ship locates a pirate ship at a distance 560 m. It fires a cannon ball with an initial speed 82 m/s. At what angle from horizontal the ball must be fired so that it hits the pirate ship
A.
$54^{\circ}$
B.
$125^{\circ}$
C.
$27^{\circ}$
D.
$18^{\circ}$
DUMET 2009 Q124 Errorless 5. Critical Thinking MCQ
On the centre of a frictionless table a small hole is made, through which a weightless string of length 2l is inserted. On the two ends of the string two balls of the same mass m are attached. Arrangement is made in such a way that half of the string is on the table top and half is hanging below. The ball on the table top is made to move in a circular path with a constant speed v. What is the centripetal acceleration of the moving ball
A.
mvl
B.
g
C.
Zero
D.
2mvl
IIT-JEE 2009 Q125 Errorless 5. Critical Thinking MCQ
A piece of wire is bent in the shape of a parabola $y = kx^{2}$ (y-axis vertical) with a bead of mass m on it. The bead can slide on the wire without friction. It stays at the lowest point of the parabola when the wire is at rest. The wire is now accelerated parallel to the x-axis with a constant acceleration a. The distance of the new equilibrium position of the bead, where the bead can stay at rest with respect to the wire, from the y-axis is
A.
$a / gk$
B.
$a / 2gk$
C.
$2a / gk$
D.
$a / 4gk$