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Kinematics-1D

346 Questions Start Allen Test
All Exams Allen Objective Errorless
Q201 Allen 6. GROUND TO GROUND PROJECTION MCQ
Three particles A, B and C are projected from the same point with the same initial speeds making angles $30^{\circ}$ , $45^{\circ}$ and $60^{\circ}$ respectively with the horizontal. Which of the following statements are correct?
A.
A, B and C have unequal ranges
B.
Ranges of A and C are equal and less than that of B
C.
Ranges of A and C are equal and greater than that of B
D.
A, B and C have equal ranges
Q202 Allen 6. GROUND TO GROUND PROJECTION MCQ
A number of bullets are fired in all possible directions with the same initial velocity u. The maximum area of ground covered by bullets is:-
A.
$\pi\left(\frac{2u^{2}}{g}\right)^{2}$
B.
$3\pi\left(\frac{u}{g}\right)^{2}$
C.
$5\pi\left(\frac{u}{2g}\right)^{2}$
D.
$\pi\left(\frac{u^{2}}{g}\right)^{2}$
Q203 Allen 6. GROUND TO GROUND PROJECTION MCQ
Four bodies P, Q, R and S are projected with equal speed 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
Q204 Allen 6. GROUND TO GROUND PROJECTION MCQ
A boy can throw a stone up to a maximum height of 10 m. The maximum horizontal distance up to which the boy can throw the same stone will be :
A.
$20\sqrt{2}$ m
B.
10 m
C.
$10\sqrt{2}$ m
D.
20 m
Q205 Allen 6. GROUND TO GROUND PROJECTION MCQ
A cricketer can throw a ball to a maximum horizontal distance of 100m. How much high above the ground can the cricketer throw the same ball :-
A.
200m
B.
400m
C.
100m
D.
50m
Q206 Allen 6. GROUND TO GROUND PROJECTION MCQ
The cannon was set by mistake at $30^{\circ}$ instead of $20^{\circ}$ with the horizontal and was fired to hit the enemy target. The cannon-shell will now fall at :
A.
The enemy target
B.
Before the enemy target
C.
Beyond the enemy target
D.
May fall at any place
Q207 Allen 6. GROUND TO GROUND PROJECTION MCQ
Two similar cannon simultaneously fires two identical cannon balls at target 1 and 2 as shown in the figure. If the cannon balls have identical initial speeds, which of the following statements is true?
A.
Target 2 is hit before target 1
B.
Target 1 is hit before target 2
C.
Both are hit at the same time
D.
information is insufficient
Q208 Allen 6. GROUND TO GROUND PROJECTION MCQ
If R is the horizontal range of a particle projected at an angle $53^{\circ}$ from horizontal, then the greatest height attained by it is:
A.
$\frac{R}{3}$
B.
2R
C.
$\frac{R}{2}$
D.
$\frac{R}{4}$
Q209 Allen 6. GROUND TO GROUND PROJECTION MCQ
A projectile can have the same range R for two angles of projection. If $h_{1}$ and $h_{2}$ be the maximum height in the two cases, then:
A.
$h_{1}h_{2} \propto R^{2}$
B.
$h_{1}h_{2} \propto R$
C.
$h_{1}h_{2} \propto \frac{1}{R}$
D.
$h_{1}h_{2} \propto \frac{1}{R^{2}}$
Q210 Allen 6. GROUND TO GROUND PROJECTION MCQ
A body is thrown with some velocity from the ground. Maximum height attained when it is thrown at $37^{\circ}$ to the horizontal is 90 m. What is the height attained when it is thrown at $53^{\circ}$ to the horizontal?
A.
90 m
B.
45 m
C.
120 m
D.
160 m
Q211 Allen 6. GROUND TO GROUND PROJECTION MCQ
Two stones are projected with the same speed but making different angles with the horizontal. Their ranges are equal. If the angle of projection of one is $\frac{\pi}{6}$ and its maximum height is $y_{1}$ , then the maximum height of the other will be:
A.
$3y_{1}$
B.
$2y_{1}$
C.
$\frac{y_{1}}{2}$
D.
$\frac{y_{1}}{3}$
Q212 Allen 6. GROUND TO GROUND PROJECTION MCQ
A ball is thrown at different angles with the same speed u and from the same point; it has the same range in both the cases. If $y_{1}$ and $y_{2}$ be the heights attained in the two cases, then $y_{1} + y_{2} = \ldots$ :
A.
$\frac{u^{2}}{g}$
B.
$\frac{2u^{2}}{g}$
C.
$\frac{u^{2}}{2g}$
D.
$\frac{u^{2}}{4g}$
Q213 Allen 6. GROUND TO GROUND PROJECTION MCQ
A body is projected at such an angle that the horizontal range is four times the greatest height. The angle of projection is:-
A.
$25^{\circ}$
B.
$33^{\circ}$
C.
$45^{\circ}$
D.
$53^{\circ}$
Q214 Allen 6. GROUND TO GROUND PROJECTION MCQ
The horizontal range of a projectile is $4\sqrt{3}$ times of its maximum height. Its angle of projection from horizontal will be:
A.
$45^{\circ}$
B.
$60^{\circ}$
C.
$90^{\circ}$
D.
$30^{\circ}$
Q215 Allen 6. GROUND TO GROUND PROJECTION MCQ
A projectile have range double as compare to its maximum height attained. The angle of projection from horizontal is-
A.
$\tan^{-1}(2)$
B.
$\tan^{-1}(4)$
C.
$\tan^{-1}(3)$
D.
$\tan^{-1}(5)$
Q216 Allen 6. GROUND TO GROUND PROJECTION MCQ
The speed of a projectile at its maximum height is $\frac{\sqrt{3}}{2}$ times its initial speed. If the range of the projectile is 'P' times the maximum height attained by it, then P equals to -
A.
$\frac{4}{3}$
B.
$2\sqrt{3}$
C.
$4\sqrt{3}$
D.
$\frac{3}{4}$
Q217 Allen 6. GROUND TO GROUND PROJECTION MCQ
A ball is projected to attain the maximum range. If the height attained is H, the range is
A.
H
B.
2H
C.
4H
D.
H/2
Q218 Allen 6. GROUND TO GROUND PROJECTION MCQ
The equation of a projectile is $y = x - \frac{gx^2}{2}$ . The angle of projection is:
A.
30Ā°
B.
60Ā°
C.
45Ā°
D.
none
Q219 Allen 6. GROUND TO GROUND PROJECTION MCQ
The equation of a projectile is $y = 4x - \frac{x^{2}}{4}$ . The horizontal range is:
A.
16 m
B.
8 m
C.
64 m
D.
12.8 m
Q220 Allen 6. GROUND TO GROUND PROJECTION MCQ
A particle is projected at an angle of $45^{\circ}$ from horizontal, 6m away from the foot of a wall, just touches the top of the wall and falls on the ground on the opposite side at a distance 3m from it. The height of wall is:
A.
2m
B.
$\frac{4}{3}$ m
C.
$\frac{8}{3}$ m
D.
$\frac{3}{4}$ m
Q221 Allen 6. GROUND TO GROUND PROJECTION MCQ
A stone is projected from the ground with velocity 50 m/s at an angle of $30^{\circ}$ from horizontal. It crosses a wall after 3 sec. How far beyond the wall the stone will strike the ground (g = 10m/sec $^{2}$ )
A.
90.2 m
B.
89.6 m
C.
86.6 m
D.
70.2 m
Q222 Allen 6. GROUND TO GROUND PROJECTION MCQ
A shell fired from the ground is just able to cross the top of a wall 90m away and 45 m high moving horizontally. The direction of projection of the shell from horizontal will be :-
A.
$25^{\circ}$
B.
$30^{\circ}$
C.
$60^{\circ}$
D.
$45^{\circ}$
Q223 Allen 6. GROUND TO GROUND PROJECTION MCQ
An arrow is shot into the air. Its range is 100 metres and its time of flight is 5 s. If the value of g is assumed to be $10 \, m/s^{2}$ , then the horizontal component of the velocity of arrow is:
A.
40 m/s
B.
20 m/s
C.
31.25 m/s
D.
12.5 m/s
Q224 Allen 6. GROUND TO GROUND PROJECTION MCQ
An arrow is shot into the air. Its range is 100 metres and its time of flight is 5 s. If the value of g is assumed to be $10 \, m/s^{2}$ , the maximum height attained by the arrow is:
A.
25 m
B.
20 m/s
C.
31.25 m
D.
12.5 m
Q225 Allen 6. GROUND TO GROUND PROJECTION MCQ
An arrow is shot into the air. Its range is 100 metres and its time of flight is 5 s. If the value of g is assumed to be $10 \, m/s^{2}$ , the vertical component of the projection velocity is:
A.
25 m/s
B.
40 m/s
C.
12.5 m/s
D.
31.25 m/s