← Back to Physics-I

Kinematics-2D

127 Questions Start Objective Test
All Exams Allen Objective Errorless
Q76 Objective 1. Taking it together MCQ
A ball is thrown from a point with a speed $v_{0}$ at an angle of projection $\theta$ . From the same point and at the same instant, a person starts running with a constant speed $v_{0}/2$ to catch the ball. Will the person be able to catch the ball? If yes, what should be the angle of projection?
A.
Yes, $60^{\circ}$
B.
Yes, $30^{\circ}$
C.
No
D.
Yes, $45^{\circ}$
Q77 Objective 1. Taking it together MCQ
The initial velocity of a particle of mass 2 kg is $(4\hat{\mathbf{i}} + 4\hat{\mathbf{j}})\ \mathrm{ms}^{-1}$ . A constant force of $-20\hat{\mathbf{j}}\ N$ is applied on the particle. Initially, the particle was at $(0, 0)$ . Find the x-coordinate of the point, where its y-coordinate is again zero.
A.
3.2 m
B.
6 m
C.
4.8 m
D.
1.2 m
Q78 Objective 1. Taking it together MCQ
An object of mass m is projected with a momentum p at such an angle that its maximum height is 1/4th of its horizontal range. Its minimum kinetic energy in its path will be
A.
$\frac{p^{2}}{8m}$
B.
$\frac{p^{2}}{4m}$
C.
$\frac{3p^{2}}{4m}$
D.
$\frac{p^{2}}{m}$
Q79 Objective 1. Taking it together MCQ
The equation of motion of a projectile are given by $x = 36 \, t \, \text{m}$ and $2y = 96 \, t - 9.8 \, t^2 \, \text{m}$ . The angle of projection is
A.
$\sin^{-1} \left( \frac{4}{5} \right)$
B.
$\sin^{-1} \left( \frac{3}{5} \right)$
C.
$\sin^{-1} \left( \frac{4}{3} \right)$
D.
$\sin^{-1} \left( \frac{3}{4} \right)$
Q80 Objective 1. Taking it together MCQ
Two stones are projected so as to reach the same distance from the point of projection on a horizontal surface. The maximum height reached by one exceeds the other by an amount equal to half the sum of the height attained by them. Then, angle of projection of the stone which attains smaller height is
A.
$45^{\circ}$
B.
$60^{\circ}$
C.
$30^{\circ}$
D.
$\tan^{-1}(3/4)$
Q81 Objective 1. Taking it together MCQ
An arrow is shot into air. Its range is 200 m and its time of flight is 5 s. If $g = 10 \, ms^{-2}$ , then horizontal component of velocity and the maximum height will be respectively
A.
$20 \, ms^{-1}$ , 62.50 m
B.
$40 \, ms^{-1}$ , 31.25 m
C.
$80 \, ms^{-1}$ , 62.5 m
D.
None of these
Q82 Objective 1. Taking it together MCQ
A body is projected from the ground with a velocity $\mathbf{v} = (3\hat{\mathbf{i}} + 10\hat{\mathbf{j}}) \, \text{ms}^{-1}$ . The maximum height attained and the range of the body respectively are (Take, $g = 10 \, ms^{-2}$ )
A.
5 m and 6 m
B.
3 m and 10 m
C.
6 m and 5 m
D.
3 m and 5 m
Q83 Objective 1. Taking it together MCQ
A cricket fielder can throw the cricket ball with a speed $v_{0}$ . If he throws the ball while running with speed $u$ at an angle $\theta$ to the horizontal, what is the effective angle to the horizontal at which the ball is projected in air as seen by a spectator? [NCERT Exemplar]
A.
$\tan^{-1}\left(\frac{v_{0}\cos\theta}{u + v_{0}\sin\theta}\right)$
B.
$\tan^{-1}\left(\frac{v_{0}\sin\theta}{u + v_{0}\cos\theta}\right)$
C.
$\tan^{-1}\left(\frac{u}{v_{0}\cos\theta + v_{0}\sin\theta}\right)$
D.
$\tan^{-1}\left(\frac{v_{0}\sin\theta + v_{0}\cos\theta}{u}\right)$
Q84 Objective 1. Taking it together MCQ
A particle is projected with a velocity of $30 \, ms^{-1}$ , at an angle of $\theta_{0} = \tan^{-1} \left( \frac{3}{4} \right)$ . After 1 s, the particle is moving at an angle $\theta$ to the horizontal, where $\tan\theta$ will be equal to (Take, $g = 10 \, ms^{-2}$ )
A.
1
B.
2
C.
$\frac{1}{2}$
D.
$\frac{1}{3}$
Q85 Objective 1. Taking it together MCQ
A bomber plane moves horizontally with a speed of $500 \, ms^{-1}$ and a bomb released from it, strikes the ground in 10 s. Angle at which it strikes the ground will be (Take, $g = 10 \, ms^{-2}$ )
A.
$\tan^{-1}\left(\frac{1}{5}\right)$
B.
$\tan^{-1}\left(\frac{1}{2}\right)$
C.
$\tan^{-1}(1)$
D.
$\tan^{-1}(5)$
Q86 Objective 1. Taking it together MCQ
Two balls are thrown simultaneously from ground with same velocity of $10 \, ms^{-1}$ but different angles of projection with horizontal. Both balls fall at same distance $5\sqrt{3} \, m$ from point of projection. What is the time interval between balls striking the ground?
A.
$(\sqrt{3}-1) \, s$
B.
$(\sqrt{3}+1) \, s$
C.
$\sqrt{3} \, s$
D.
$1 \, s$
Q87 Objective 1. Taking it together MCQ
A particle moves along a parabolic path $y = -9x^{2}$ in such a way that the x-component of velocity remains constant and has a value $1/3 \, ms^{-1}$ . The acceleration of the particle is
A.
$\frac{1}{3} \, ms^{-2}$
B.
$3 \, ms^{-2}$
C.
$\frac{2}{3} \, ms^{-2}$
D.
$2 \, ms^{-2}$
Q88 Objective 1. Taking it together MCQ
A projectile can have same range from two angles of projection with same initial speed. If $h_{1}$ and $h_{2}$ be the maximum heights, then
A.
$R = \sqrt{h_{1} h_{2}}$
B.
$R = \sqrt{2 h_{1} h_{2}}$
C.
$R = 2\sqrt{h_{1} h_{2}}$
D.
$R = 4\sqrt{h_{1} h_{2}}$
Q89 Objective 1. Taking it together MCQ
A ball is projected from ground with a speed of $20 \, ms^{-1}$ at an angle of $45^{\circ}$ with horizontal. There is a wall of 25 m height at a distance of 10 m from the projection point. The ball will hit the wall at a height of
A.
5 m
B.
7.5 m
C.
10 m
D.
12.5 m
Q90 Objective 1. Taking it together MCQ
A boy can throw a stone up to a maximum height of 10 m. The maximum horizontal distance that the boy can throw the same stone up to will be
A.
$20\sqrt{2}$ m
B.
10 m
C.
$10\sqrt{2}$ m
D.
20 m
Q91 Objective 1. Taking it together MCQ
At the height 80 m, an aeroplane is moving with $150 \, ms^{-1}$ . A bomb is dropped from it so as to hit a target. At what distance from the target should the bomb be dropped? (Take, $g = 10 \, ms^{-2}$ )
A.
605.3 m
B.
600 m
C.
80 m
D.
230 m
Q92 Objective 1. Taking it together MCQ
A ball is projected upwards from the top of a tower with velocity $25 \, ms^{-1}$ making an angle of $30^\circ$ with the horizontal. If the height of the tower is 70 m, after what time from the instant of throwing, will the ball reach the ground? (Take, $g = 10 \, ms^{-2}$ )
A.
2 s
B.
5 s
C.
7 s
D.
9 s
Q93 Objective 1. Taking it together MCQ
From the top of a tower of height 40 m, a ball is projected upwards with a speed of $20 \, ms^{-1}$ at an angle of elevation of $30^\circ$ . The ratio of the total time taken by the ball to hit the ground to its time of flight (time taken to come back to the same elevation) is (Take, $g = 10 \, ms^{-2}$ )
A.
2:1
B.
3:1
C.
3:2
D.
1.5:1
Q94 Objective 1. Taking it together MCQ
The coordinates of a moving particle at any time t are given by x = ct and $y = bt^{2}$ . The speed of the particle is given by
A.
$2t\sqrt{b^{2}-c^{2}}$
B.
$\sqrt{4b^{2}t^{2}+c^{2}}$
C.
$2t(b+c)$
D.
$2t(b-c)$
Q95 Objective 1. Taking it together MCQ
A ball rolls off the edge of a horizontal table top 4 m high. If it strikes the floor at a point 5 m horizontally away from the edge of the table, what was its speed at the instant it left the table?
A.
$2.5 \, ms^{-1}$
B.
$3.5 \, ms^{-1}$
C.
$5.55 \, ms^{-1}$
D.
$6.5 \, ms^{-1}$
Q96 Objective 1. Taking it together MCQ
A ball is thrown from the ground to a wall 3 m high at a distance of 6 m and falls 18 m away from the wall, the angle of projection of ball is
A.
$\tan^{-1}\left(\frac{3}{2}\right)$
B.
$\tan^{-1}\left(\frac{2}{3}\right)$
C.
$\tan^{-1}\left(\frac{1}{2}\right)$
D.
$\tan^{-1}\left(\frac{3}{4}\right)$
Q97 Objective 1. Taking it together MCQ
The horizontal range and maximum height attained by a projectile are R and H, respectively. If a constant horizontal acceleration a = g/4 is imparted to the projectile due to wind, then its horizontal range and maximum height will be
A.
$(R + H), \frac{H}{2}$
B.
$\left(R + \frac{H}{2}\right), 2H$
C.
$(R + 2H), H$
D.
$(R + H), H$
Q98 Objective 1. Taking it together MCQ
An object is projected with a velocity of $20 \, ms^{-1}$ making an angle of $45^{\circ}$ with horizontal. The equation for trajectory is $h = Ax - Bx^{2}$ , where h is height, x is horizontal distance, A and B are constants. The ratio A : B is (Take, $g = 10 \, ms^{-2}$ )
A.
1:5
B.
5:1
C.
1:40
D.
40:1
Q99 Objective 1. Taking it together MCQ
If the instantaneous velocity of a particle projected as shown in figure is given by $\mathbf{v} = a\hat{\mathbf{i}} + (b - ct)\hat{\mathbf{j}}$ . where $a, b$ and $c$ are positive constants, the range on the horizontal plane will be
A.
2ab/c
B.
ab/c
C.
ac/b
D.
a/2bc
Q100 Objective 1. Taking it together MCQ
Two particles are simultaneously projected in opposite directions horizontally from a given point in space, where gravity g is uniform. If $u_{1}$ and $u_{2}$ be their initial speeds, then the time t after which their velocities are mutually perpendicular is given by
A.
$\frac{\sqrt{u_{1}u_{2}}}{g}$
B.
$\frac{\sqrt{u_{1}^{2}+u_{2}^{2}}}{g}$
C.
$\frac{\sqrt{u_{1}(u_{1}+u_{2})}}{g}$
D.
$\frac{\sqrt{u_{2}(u_{1}+u_{2})}}{g}$