← Back to Physics-I

Kinematics-2D

384 Questions Start Objective Test
All Exams Allen Objective Errorless
Q276 Objective Taking it together MCQ
A body is thrown horizontally from the top of a tower of height 5 m. It touches the ground at a distance of 10 m from the foot of the tower. The initial velocity of the body is (Take, $g = 10 \, ms^{-2}$ )
A.
$2.5 \, ms^{-1}$
B.
$5 \, ms^{-1}$
C.
$10 \, ms^{-1}$
D.
$20 \, ms^{-1}$
Q277 Objective Taking it together MCQ
Velocity and acceleration of a particle at some instant of time are $\mathbf{v} = (3\hat{\mathbf{i}} + 4\hat{\mathbf{j}}) \, \text{ms}^{-1}$ and $\mathbf{a} = -(6\hat{\mathbf{i}} + 8\hat{\mathbf{j}}) \, \text{ms}^{-2}$ , respectively. At the same instant particle is at origin, maximum x-coordinate of particle will be
A.
1.5 m
B.
0.75 m
C.
2.25 m
D.
4 m
Q278 Objective Taking it together MCQ
Two paper screens A and B are separated by a distance of 100 m. A bullet pierces A and then B. The hole in B is 10 cm below the hole in A. If the bullet is travelling horizontally at the time of hitting A, then the velocity of the bullet at A is
A.
$100 \, ms^{-1}$
B.
$200 \, ms^{-1}$
C.
$600 \, ms^{-1}$
D.
$700 \, ms^{-1}$
Q279 Objective Taking it together MCQ
Two stones having different masses $m_{1}$ and $m_{2}$ are projected at an angle $\alpha$ and $(90^{\circ}-\alpha)$ with same speed from same point. The ratio of their maximum heights is
A.
1:1
B.
$1:\tan\alpha$
C.
$\tan\alpha:1$
D.
$\tan^{2}\alpha:1$
Q280 Objective Taking it together MCQ
Two projectiles A and B are thrown from the same point with velocities v and v/2, respectively. If B is thrown at an angle $45^{\circ}$ with horizontal, what is the inclination of A when their ranges are the same?
A.
$\sin^{-1}\left(\frac{1}{4}\right)$
B.
$\frac{1}{2}\sin^{-1}\left(\frac{1}{4}\right)$
C.
$2\sin^{-1}\left(\frac{1}{4}\right)$
D.
$\frac{1}{2}\sin^{-1}\left(\frac{1}{8}\right)$
Q281 Objective Taking it together MCQ
A particle moves in the XY-plane according to the law $x = kt$ , $y = kt(1 - \alpha t)$ , where $k$ and $\alpha$ are positive constants and $t$ is time. The trajectory of the particle is
A.
$y = kx$
B.
$y = x - \frac{\alpha x^2}{k}$
C.
$y = -\frac{ax^2}{k}$
D.
$y = \alpha x$
Q282 Objective Taking it together MCQ
The maximum range of a gun on horizontal terrain is 1 km. If $g = 10 \, ms^{-2}$ , what must be the muzzle velocity of the shell?
A.
$400 \, ms^{-1}$
B.
$200 \, ms^{-1}$
C.
$100 \, ms^{-1}$
D.
$50 \, ms^{-1}$
Q283 Objective Taking it together MCQ
The equation of trajectory of a projectile is $y = \sqrt{3} x - \frac{g}{2} x^2$ , the angle of its projection is
A.
$90^\circ$
B.
zero
C.
$60^\circ$
D.
$30^\circ$
Q284 Objective Taking it together MCQ
A projectile is thrown upward with a velocity $v_{0}$ at an angle $\alpha$ to the horizontal. The change in velocity of the projectile when it strikes the same horizontal plane is
A.
$v_{0} \sin \alpha$ vertically downward
B.
$2v_{0} \sin \alpha$ vertically downward
C.
$2v_{0} \sin \alpha$ vertically upward
D.
zero
Q285 Objective Taking it together MCQ
The maximum height attained by a projectile is increased by 10% by increasing its speed of projection, without changing the angle of projection. The percentage increase in the horizontal range will be
A.
20%
B.
15%
C.
10%
D.
5%
Q286 Objective Taking it together MCQ
A body is projected at an angle of $30^{\circ}$ with the horizontal with momentum p. At its highest point, the magnitude of the momentum is
A.
$\frac{\sqrt{3}}{2}p$
B.
$\frac{2}{\sqrt{3}}p$
C.
p
D.
$\frac{p}{2}$
Q287 Objective Taking it together MCQ
A projectile is fired from ground level at an angle $\theta$ above the horizontal. The elevation angle $\phi$ of the highest point as seen from the launch point is related to $\theta$ by the relation
A.
$\tan \phi = \frac{1}{4} \tan \theta$
B.
$\tan \phi = \tan \theta$
C.
$\tan \phi = \frac{1}{2} \tan \theta$
D.
$\tan \phi = 2 \tan \theta$
Q288 Objective Taking it together MCQ
A ball is thrown up with a certain velocity at an angle $\theta$ to the horizontal. The kinetic energy KE of the ball varies with horizontal displacement x as
A.
B.
C.
D.
Q289 Objective Taking it together MCQ
A body projected with velocity u at projection angle $\theta$ has horizontal range R. For the same velocity and projection angle, its range on the moon surface will be $(g_{\text{moon}} = g_{\text{earth}} / 6)$
A.
36R
B.
$\frac{R}{36}$
C.
$\frac{R}{16}$
D.
6R
Q290 Objective Taking it together MCQ
Three balls of same masses are projected with equal speeds at angle $15^{\circ}$ , $45^{\circ}$ , $75^{\circ}$ , and their ranges are respectively $R_{1}$ , $R_{2}$ and $R_{3}$ , then
A.
$R_{1} > R_{2} > R_{3}$
B.
$R_{1} < R_{2} < R_{3}$
C.
$R_{1} = R_{2} = R_{3}$
D.
$R_{1} = R_{3} < R_{2}$
Q291 Objective Taking it together MCQ
A projectile is thrown with an initial velocity of $(a\hat{\mathbf{i}}+b\hat{\mathbf{j}})\mathrm{ms}^{-1}$ . 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
Q292 Objective Taking it together MCQ
The ratio of the speed of a projectile at the point of projection to the speed at the top of its trajectory is x. The angle of projection with the horizontal is
A.
$\sin^{-1}x$
B.
$\cos^{-1}x$
C.
$\sin^{-1}(1/x)$
D.
$\cos^{-1}(1/x)$
Q293 Objective Taking it together MCQ
A man can throw a stone such that it acquires maximum horizontal range 80 m. The maximum height to which it will rise for the same projectile (in metre) is
A.
10
B.
20
C.
40
D.
50
Q294 Objective Taking it together MCQ
The velocity at the maximum height of a projectile is half of its initial velocity of projection (u). Its range on horizontal plane is
A.
$\frac{3u^{2}}{g}$
B.
$\frac{3}{2}\cdot\frac{u^{2}}{g}$
C.
$\frac{u^{2}}{3g}$
D.
$\frac{\sqrt{3}}{2}\cdot\frac{u^{2}}{g}$
Q295 Objective Taking it together MCQ
A projectile is thrown from a point in a horizontal plane such that the horizontal and vertical velocities are $9.8 \, ms^{-1}$ and $19.6 \, ms^{-1}$ . It will strike the plane after covering distance of
A.
39.2 m
B.
19.6 m
C.
9.8 m
D.
4.9 m
Q296 Objective Taking it together MCQ
The greatest height to which a man can throw a stone is h. The greatest distance to which he can throw it will be
A.
$\frac{h}{2}$
B.
h
C.
2h
D.
3h
Q297 Objective Taking it together MCQ
Four bodies P, Q, R and S are projected with equal velocities having angles of projection $15^{\circ}$ , $30^{\circ}$ , $45^{\circ}$ and $60^{\circ}$ with the horizontal respectively. The body having shortest range is
A.
P
B.
Q
C.
R
D.
S
Q298 Objective Taking it together MCQ
A stone is projected in air. Its time of flight is 3 s and range is 150 m. Maximum height reached by the stone is (Take, $g = 10 \, ms^{-2}$ )
A.
37.5 m
B.
22.5 m
C.
90 m
D.
11.25 m
Q299 Objective Taking it together MCQ
A boy throws a ball with a velocity u at an angle $\theta$ with the horizontal. 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.
$u \cos \theta$
B.
$u \sin \theta$
C.
$u \tan \theta$
D.
$u \sec \theta$
Q300 Objective Taking it together MCQ
Galileo writes that for angle of projection of a projectile at angle $(45^{\circ}-\theta)$ and $(45^{\circ}+\theta)$ , the horizontal ranges described by the projectile are in the ratio of (if $\theta\leq45^{\circ}$ )
A.
2:1
B.
1:2
C.
1:1
D.
2:3