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Kinematics-2D

244 Questions Start Advance Test
All Exams Allen Advance Errorless
Q176 Advance 3. REASONING BASED QUESTIONS MCQ
Statement-1: A coin is allowed to fall in a train moving with constant velocity. Its trajectory is parabola as seen by an observer sitting in the train. Statement-2: An observer on ground will see the path of coin as a parabola.
A.
If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.
B.
If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.
C.
If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.
D.
If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.
Q177 Advance 3. REASONING BASED QUESTIONS MCQ
Statement-1: A particle is projected with a velocity u making at an angle $\theta < 90^{\circ}$ with the horizontal. When particle strikes the ground its speed is again u. Statement-2: Velocity along horizontal direction remains same but velocity along vertical direction is changed. When particle strikes the ground, magnitude of final vertical velocity is equal to magnitude of initial vertical velocity.
A.
If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.
B.
If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.
C.
If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.
D.
If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.
Q178 Advance 3. REASONING BASED QUESTIONS MCQ
Statement-1: Two particles of different mass, projected with same velocity at same angles. The maximum height attained by both the particles will be same. Statement-2: The maximum height of projectile is independent of the mass of the particle.
A.
If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.
B.
If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.
C.
If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.
D.
If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.
Q179 Advance 3. REASONING BASED QUESTIONS MCQ
Statement-1: When speed of projection of a body is made n-times, its time of flight becomes n times Statement-2: This is because range of projectile become n times.
A.
If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.
B.
If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.
C.
If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.
D.
If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.
Q180 Advance 3. REASONING BASED QUESTIONS MCQ
Statement-1: Horizontal velocity of a particle moving under the influence of gravity remains constant. Statement-2: Acceleration due to gravity acts vertically downwards.
A.
If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.
B.
If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.
C.
If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.
D.
If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.
Q181 Advance 3. REASONING BASED QUESTIONS MCQ
Statement-1: An oblique projectile is launched from the ground to attain a maximum range. The maximum height attained by the projectile is 25% of range. Statement-2: $R = \frac{u^{2} \sin(2\theta)}{g}$ and $H = \frac{u^{2} \sin^{2} \theta}{2g}$
A.
If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.
B.
If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.
C.
If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.
D.
If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.
Q182 Advance 4. LINKED COMPREHENSION TYPE QUESTIONS MCQ

Comprehension Passage: Comprehension - 1

A point moves in the plane x, y according to the law $x = kt$ , $y = kt(1 - \alpha t)$ , where k and $\alpha$ are positive constants and t is the time. Based on the above facts, answer the following questions. The trajectory $y(x)$ followed by the particle is a/an
A.
straight line
B.
ellipse
C.
parabola
D.
cycloid
Q183 Advance 4. LINKED COMPREHENSION TYPE QUESTIONS MCQ

Comprehension Passage: Comprehension - 1

A point moves in the plane x, y according to the law $x = kt$ , $y = kt(1 - \alpha t)$ , where k and $\alpha$ are positive constants and t is the time. Based on the above facts, answer the following questions. The velocity $v$ of the point is minimum at time
A.
$t = \frac{1}{\alpha}$
B.
$t = \frac{1}{2\alpha}$
C.
$t = \frac{2}{\alpha}$
D.
$t = \frac{1}{3\alpha}$
Q184 Advance 4. LINKED COMPREHENSION TYPE QUESTIONS MCQ

Comprehension Passage: Comprehension - 1

A point moves in the plane x, y according to the law $x = kt$ , $y = kt(1 - \alpha t)$ , where k and $\alpha$ are positive constants and t is the time. Based on the above facts, answer the following questions. The acceleration of the particle at time when the velocity has a minimum value is
A.
$(2 k \alpha) \hat {j}$
B.
$(k \alpha) \hat {j}$
C.
$\left(\frac {k \alpha}{2}\right) \hat {j}$
D.
$- 2 (k \alpha) \hat {j}$
Q185 Advance 4. LINKED COMPREHENSION TYPE QUESTIONS MCQ

Comprehension Passage: Comprehension - 1

A point moves in the plane x, y according to the law $x = kt$ , $y = kt(1 - \alpha t)$ , where k and $\alpha$ are positive constants and t is the time. Based on the above facts, answer the following questions. The moment $t_0$ at which the velocity vector forms an angle $\frac{\pi}{4}$ with the acceleration vector is
A.
$\frac{1}{\alpha}$
B.
$\frac{1}{2\alpha}$
C.
$\frac{2}{\alpha}$
D.
$\frac{1}{3\alpha}$
Q186 Advance 4. LINKED COMPREHENSION TYPE QUESTIONS MCQ

Comprehension Passage: Comprehension - 2

A particle is projected from a point A with velocity $u\sqrt{2}$ at an angle of $45^{\circ}$ with horizontal as shown in figure. It strikes the plane BC at right angles. Based on the above facts, answer the following questions. The velocity of the particle at the time of collision is
A.
u
B.
$\frac{u}{2}$
C.
$\frac{\sqrt{3}u}{2}$
D.
$\frac{2u}{\sqrt{3}}$
Q187 Advance 4. LINKED COMPREHENSION TYPE QUESTIONS MCQ

Comprehension Passage: Comprehension - 2

A particle is projected from a point A with velocity $u\sqrt{2}$ at an angle of $45^{\circ}$ with horizontal as shown in figure. It strikes the plane BC at right angles. Based on the above facts, answer the following questions. The time after which collision takes place is
A.
$\frac{u}{g}$
B.
$\frac{\sqrt{3}u}{g}$
C.
$\frac{u}{g}\left(\frac{\sqrt{3}+1}{\sqrt{3}}\right)$
D.
$\left(\frac{\sqrt{3}}{\sqrt{3}-1}\right)\frac{u}{g}$
Q188 Advance 4. LINKED COMPREHENSION TYPE QUESTIONS MCQ

Comprehension Passage: Comprehension - 3

An oblique projectile is launched from a point O with an initial velocity u that makes an angle $\theta$ with the horizontal. It is observed that the projectile attains a maximum height H at the point $\left(\frac{R}{2}, H\right)$ , where R is the maximum distance from O at which the projectile strikes the ground. Now, if the velocity of the projectile is $\vec{v} = (20\hat{i} + 10\hat{j}) \, \text{ms}^{-1}$ when it is at a height of 15 m above the ground, then based on this information and taking $g = 10 \, ms^{-2}$ , answer the following questions. The launch speed in $\mathrm{ms}^{-1}$ is
A.
$20\mathrm{ms}^{-1}$
B.
$20\sqrt{2}\mathrm{ms}^{-1}$
C.
$40\mathrm{ms}^{-1}$
D.
$40\sqrt{2}\mathrm{ms}^{-1}$
Q189 Advance 4. LINKED COMPREHENSION TYPE QUESTIONS MCQ

Comprehension Passage: Comprehension - 3

An oblique projectile is launched from a point O with an initial velocity u that makes an angle $\theta$ with the horizontal. It is observed that the projectile attains a maximum height H at the point $\left(\frac{R}{2}, H\right)$ , where R is the maximum distance from O at which the projectile strikes the ground. Now, if the velocity of the projectile is $\vec{v} = (20\hat{i} + 10\hat{j}) \, \text{ms}^{-1}$ when it is at a height of 15 m above the ground, then based on this information and taking $g = 10 \, ms^{-2}$ , answer the following questions. The value of $\theta$ (in radian) is
A.
$\frac{\pi}{6}$
B.
$\frac{\pi}{4}$
C.
$\frac{\pi}{3}$
D.
$\frac{2\pi}{3}$
Q190 Advance 4. LINKED COMPREHENSION TYPE QUESTIONS MCQ

Comprehension Passage: Comprehension - 3

An oblique projectile is launched from a point O with an initial velocity u that makes an angle $\theta$ with the horizontal. It is observed that the projectile attains a maximum height H at the point $\left(\frac{R}{2}, H\right)$ , where R is the maximum distance from O at which the projectile strikes the ground. Now, if the velocity of the projectile is $\vec{v} = (20\hat{i} + 10\hat{j}) \, \text{ms}^{-1}$ when it is at a height of 15 m above the ground, then based on this information and taking $g = 10 \, ms^{-2}$ , answer the following questions. The coordinate, where the maximum height is attained is
A.
(80, 20) m
B.
(20, 40) m
C.
(20, 80) m
D.
(40, 20) m
Q191 Advance 4. LINKED COMPREHENSION TYPE QUESTIONS MCQ

Comprehension Passage: Comprehension - 4

Consider the situation shown in the figure. A particle has to be projected from point P in horizontal direction. It is required for the particle to strike the plane AB (see figure). The minimum value of horizontal velocity of particle at point $P$ so that particle may strike the plane $AB$ is
A.
$\sqrt{\frac{9}{8}ag}$
B.
$\sqrt{\frac{25}{8}ag}$
C.
$\sqrt{\frac{1}{2}ag}$
D.
$\sqrt{3ag}$
Q192 Advance 4. LINKED COMPREHENSION TYPE QUESTIONS MCQ

Comprehension Passage: Comprehension - 4

Consider the situation shown in the figure. A particle has to be projected from point P in horizontal direction. It is required for the particle to strike the plane AB (see figure). The time taken by particle in going from point $P$ to plane $AB$ is
A.
$4\sqrt{\frac{a}{g}}$
B.
$\sqrt{\frac{4a}{g}}$
C.
$\sqrt{\frac{2a}{g}}$
D.
$\sqrt{\frac{8a}{g}}$
Q193 Advance 4. LINKED COMPREHENSION TYPE QUESTIONS MCQ

Comprehension Passage: Comprehension - 4

Consider the situation shown in the figure. A particle has to be projected from point P in horizontal direction. It is required for the particle to strike the plane AB (see figure). The maximum value of horizontal velocity of particle at point $P$ so that it may strike the plane $AB$ is
A.
$\sqrt{\frac{9}{8}ag}$
B.
$\sqrt{\frac{25}{8}ag}$
C.
$\sqrt{\frac{1}{2}ag}$
D.
$\sqrt{3ag}$
Q194 Advance 4. LINKED COMPREHENSION TYPE QUESTIONS MCQ

Comprehension Passage: Comprehension - 5

A ball is projected horizontally from a height of 100 m from the ground with a speed of $20 \, ms^{-1}$ . Taking $g = 10 \, ms^{-2}$ and based on the information provided, answer the following questions. The time taken to reach the ground is
A.
$\sqrt{5}$ s
B.
$2\sqrt{5}$ s
C.
$3\sqrt{5}$ s
D.
$4\sqrt{5}$ s
Q195 Advance 4. LINKED COMPREHENSION TYPE QUESTIONS MCQ

Comprehension Passage: Comprehension - 5

A ball is projected horizontally from a height of 100 m from the ground with a speed of $20 \, ms^{-1}$ . Taking $g = 10 \, ms^{-2}$ and based on the information provided, answer the following questions. The horizontal distance it covers before striking the ground is
A.
$20\sqrt{5}$ m
B.
$40\sqrt{5}$ m
C.
$60\sqrt{5}$ m
D.
$80\sqrt{5}$ m
Q196 Advance 4. LINKED COMPREHENSION TYPE QUESTIONS MCQ

Comprehension Passage: Comprehension - 5

A ball is projected horizontally from a height of 100 m from the ground with a speed of $20 \, ms^{-1}$ . Taking $g = 10 \, ms^{-2}$ and based on the information provided, answer the following questions. The angle with the vertical which it strikes the ground is
A.
$\tan^{-1}\left(\frac{1}{\sqrt{3}}\right)$
B.
$\tan^{-1}\left(\frac{1}{\sqrt{2}}\right)$
C.
$\tan^{-1}\left(\frac{1}{\sqrt{5}}\right)$
D.
$\tan^{-1}\left(\frac{1}{\sqrt{7}}\right)$
Q197 Advance 4. LINKED COMPREHENSION TYPE QUESTIONS MCQ

Comprehension Passage: Comprehension - 6

For a particle moving in the x-y plane the x, y coordinates as a function of time are given by x=6t and $y=8t-5t^{2}$ , where x and y are in metre and t is in second. Assume no air drag, answer the following questions. Based on the above facts, answer the following questions. Select the correct statement from the following
A.
The particle will follow a parabolic path to have a projectile motion with an initial velocity of $5 \, ms^{-1}$ and an acceleration of $3 \, ms^{-2}$ acting along -y axis
B.
The particle will follow a parabolic path to have a projectile motion with an initial velocity of $6 \, ms^{-1}$ and a constant acceleration of $5 \, ms^{-2}$ acting along -y axis
C.
The particle will follow a parabolic path to have a projectile motion with an initial horizontal velocity of $6 \, ms^{-1}$ and a constant acceleration of $10 \, ms^{-2}$ acting along -y axis
D.
None of the above statement seems to be correct
Q198 Advance 4. LINKED COMPREHENSION TYPE QUESTIONS MCQ

Comprehension Passage: Comprehension - 6

For a particle moving in the x-y plane the x, y coordinates as a function of time are given by x=6t and $y=8t-5t^{2}$ , where x and y are in metre and t is in second. Assume no air drag, answer the following questions. Based on the above facts, answer the following questions. The velocity, of the projectile, along x-axis after 0.2 second is
A.
$>6\ ms^{-1}$
B.
$<6\ ms^{-1}$
C.
$6\ ms^{-1}$
D.
zero
Q199 Advance 4. LINKED COMPREHENSION TYPE QUESTIONS MCQ

Comprehension Passage: Comprehension - 6

For a particle moving in the x-y plane the x, y coordinates as a function of time are given by x=6t and $y=8t-5t^{2}$ , where x and y are in metre and t is in second. Assume no air drag, answer the following questions. Based on the above facts, answer the following questions. The initial vertical velocity is
A.
$6 \, ms^{-1}$
B.
$7 \, ms^{-1}$
C.
$8 \, ms^{-1}$
D.
$10 \, ms^{-1}$
Q200 Advance 4. LINKED COMPREHENSION TYPE QUESTIONS MCQ

Comprehension Passage: Comprehension - 6

For a particle moving in the x-y plane the x, y coordinates as a function of time are given by x=6t and $y=8t-5t^{2}$ , where x and y are in metre and t is in second. Assume no air drag, answer the following questions. Based on the above facts, answer the following questions. The velocity of projection of the projectile is
A.
$6 \, ms^{-1}$
B.
$7 \, ms^{-1}$
C.
$8 \, ms^{-1}$
D.
$10 \, ms^{-1}$