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Kinematics-2D

127 Questions Start Objective Test
All Exams Allen Objective Errorless
Q51 Objective 1. 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.
$R_{1} = R_{3} < R_{2}$
Q52 Objective 1. 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
Q53 Objective 1. 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.
$\cos^{-1}(1/x)$
Q54 Objective 1. 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
Q55 Objective 1. 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.
$\frac{\sqrt{3}}{2}\cdot\frac{u^{2}}{g}$
Q56 Objective 1. 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
Q57 Objective 1. 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
Q58 Objective 1. 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
Q59 Objective 1. 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
Q60 Objective 1. 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.
$u \sec \theta$
Q61 Objective 1. 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
Q62 Objective 1. Taking it together MCQ
If time of flight of a projectile is 10 s. Range is 500 m. The maximum height attained by it will be
A.
125 m
B.
50 m
C.
100 m
D.
150 m
Q63 Objective 1. Taking it together MCQ
A body of mass m is thrown upwards at an angle $\theta$ with the horizontal with velocity v. While rising up the velocity of the mass after t seconds will be
A.
$\sqrt{(v\cos\theta)^{2}+(v\sin\theta)^{2}}$
B.
$\sqrt{(v\cos\theta-v\sin\theta)^{2}-gt}$
C.
$\sqrt{v^{2}+g^{2}t^{2}-(2v\sin\theta)gt}$
D.
$\sqrt{v^{2}+g^{2}t^{2}-(2v\cos\theta)gt}$
Q64 Objective 1. Taking it together MCQ
A stone is thrown at an angle $\theta$ with the horizontal, reaches a maximum height $H$ . Then, the time of flight of stone will be
A.
$\sqrt{\frac{2H}{g}}$
B.
$2\sqrt{\frac{2H}{g}}$
C.
$\frac{2\sqrt{2H\sin\theta}}{g}$
D.
$\frac{\sqrt{2H\sin\theta}}{g}$
Q65 Objective 1. 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 height h as
A.
B.
C.
D.
Q66 Objective 1. Taking it together MCQ
For a given velocity, a projectile has the same range R for two angles of projection. If $t_{1}$ and $t_{2}$ are the time of flight in the two cases, then $t_{1}t_{2}$ is equal to
A.
$\frac{2R}{g}$
B.
$\frac{R}{g}$
C.
$\frac{4R}{g}$
D.
$\frac{R}{2g}$
Q67 Objective 1. Taking it together MCQ
A cricket ball is hit for a six by the bat at an angle of $45^{\circ}$ to the horizontal with kinetic energy K. At the highest point, the kinetic energy of the ball is
A.
zero
B.
K
C.
K/2
D.
$K/\sqrt{2}$
Q68 Objective 1. Taking it together MCQ
The equation of motion of a projectile is $y = 12x - \frac{3}{4}x^{2}$ What is the range of the projectile?
A.
12 m
B.
16 m
C.
20 m
D.
24 m
Q69 Objective 1. Taking it together MCQ
A ball of mass m is projected from the ground with an initial velocity u making an angle of $\theta$ with the vertical. What is the change in velocity between the point of projection and the highest point?
A.
$u \cos \theta$ downward
B.
$u \cos \theta$ upward
C.
$u \sin \theta$ upward
D.
$u \sin \theta$ downward
Q70 Objective 1. Taking it together MCQ
The equation of projectile is $Y = \sqrt{3}X - \frac{1}{2} gX^{2}$ . The velocity of projection is
A.
$1 \, ms^{-1}$
B.
$2 \, ms^{-1}$
C.
$3 \, ms^{-1}$
D.
$1.2 \, ms^{-1}$
Q71 Objective 1. Taking it together MCQ
The range of a projectile when launched at an angle $\theta$ is same as when launched at an angle $2\theta$ . What is the value of $\theta$ ?
A.
$15^{\circ}$
B.
$30^{\circ}$
C.
$45^{\circ}$
D.
$60^{\circ}$
Q72 Objective 1. Taking it together MCQ
A particle is thrown with a speed $u$ at an angle $\theta$ with the horizontal. When the particle makes an angle $\phi$ with the horizontal, its speed changes to $v$ , where
A.
$v = u \cos \theta$
B.
$v = u \cos \theta \cos \phi$
C.
$v = u \cos \theta \sec \phi$
D.
$v = u \sec \theta \cos \phi$
Q73 Objective 1. Taking it together MCQ
A projectile has the maximum range 500 m. If the projectile is thrown up a smooth inclined plane of $30^{\circ}$ with the same (magnitude) velocity, the distance covered by it along the inclined plane till it stops will be
A.
250 m
B.
500 m
C.
750 m
D.
1000 m
Q74 Objective 1. Taking it together MCQ
A projectile $A$ is thrown at an angle $30^{\circ}$ to the horizontal from point $P$ . At the same time, another projectile $B$ is thrown with velocity $v_{2}$ upwards from the point $Q$ vertically below the highest point $A$ would reach. For $B$ to collide with $A$ , the ratio $\frac{v_{2}}{v_{1}}$ should be
A.
$\frac{\sqrt{3}}{2}$
B.
2
C.
$\frac{1}{2}$
D.
$\frac{2}{\sqrt{3}}$
Q75 Objective 1. Taking it together MCQ
A ball is thrown from a point O aiming a target at angle $30^{\circ}$ with the horizontal, so that the ball hits the target at B but the ball hits at point A, a vertical distance h below B. If the initial velocity of the ball is $20 \, ms^{-1}$ and the horizontal distance between O and C is 10 m. Find the value of h.
A.
$\frac{g}{6}\mathrm{m}$
B.
$\frac{g}{10}\mathrm{m}$
C.
$\frac{g}{3}\mathrm{m}$
D.
$\frac{g}{12}\mathrm{m}$