Motion in a plane — DPP 1

20 NEET questions from Motion in a plane, with answers and explanations. Attempt it as a timed test to get scoring, accuracy breakdown and mistake tracking.

Attempt this test free 20 questions · 30 minutes · +80 marks
1
During projectile motion, the acceleration of a particle at the highest point of its trajectory is
  1. A g
  2. B Zero
  3. C Less than g
  4. D Dependent upon projection velocity
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Correct answer: A

2
If $\hat { i } , \hat { j }$ and $\hat { k }$ are unit vectors along X , Y & Z axis respectively, then tick the wrong statement:
  1. A $\hat { i } \cdot \hat { i } = 1$
  2. B $\hat { i } \times \hat { j } = \hat { k }$
  3. C $\hat { i } \cdot \hat { j } = 0$
  4. D $\hat { i } \times \hat { k } = - \hat { i }$
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Correct answer: D

3
The angle that the vector $\bar { A } = 2 \hat { i } + 3 \hat { j }$ makes with y-axis is:
  1. A $\tan ^ { - 1 } ( 3 / 2 )$
  2. B $\tan ^ { - 1 } ( 2 / 3 )$
  3. C $\sin ^ { - 1 } ( 2 / 3 )$
  4. D $\cos ^ { - 1 } ( 3 / 2 )$
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Correct answer: B

4
A stone is projected with a velocity 20√2 m/s at an angle of 45° the horizontal. The average velocity of stone during its motion from starting point to its maximum height is; (g = 10 m/s$^{2}$)
  1. A 10√5 m/s
  2. B 20√5 m/s
  3. C 20 m/s
  4. D 5√5 m/s
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Correct answer: A

5
The magnitudes of vectors $\bar { A } , \bar { B }$ and $\bar { C }$ are respectively 12, 5 and 13 units and $\bar { A } + \bar { B } = { } ^ { - }$, then the angle between $\bar { A }$ and $\bar { B }$ is:
  1. A 0
  2. B $\pi / 3$
  3. C $\pi / 2$
  4. D $\pi / 4$
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Correct answer: C

6
Two forces each of magnitude F have a resultant of the same magnitude F. The angle between the two forces is
  1. A $45 ^ { \circ }$
  2. B $120 ^ { \circ }$
  3. C $150 ^ { \circ }$
  4. D $60 ^ { \circ }$
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Correct answer: B

7
A cricketer can throw a ball to a maximum horizontal distance of 100 m. With the same speed how much high the above the ground can the cricketer throw the same ball in a separate throw?
  1. A 50 m
  2. B 100 m
  3. C 150 m
  4. D 200 m
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Correct answer: A

8
A particle moves along the parabolic path y = ax$^{2}$ in such a way that the x component of the velocity remains constant, say c. The acceleration of the particle is
  1. A $a c \hat{k}$
  2. B $2 a c^{2} \hat{j}$
  3. C $a c^{2} \hat{j}$
  4. D $a^{2} c \hat{j}$
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Correct answer: B

9
Vector $\bar { A }$ and $\bar { B }$ are shown in the figure. The angle between vector $\bar { A }$ and $\vec { B }$ is
Motion in a plane – NEET-17960
  1. A $60 ^ { \circ }$
  2. B $90 ^ { \circ }$
  3. C $30 ^ { \circ }$
  4. D $120 ^ { \circ }$
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Correct answer: B

10
A point mass is projected, making an acute angle with the horizontal. If angle between velocity and acceleration $\bar { g }$ is θ at any time t during the motion, then θ is given by
  1. A $0 ^ { \circ } < \theta < 90 ^ { \circ }$
  2. B $\theta = 90 ^ { \circ }$
  3. C $\theta < 90 ^ { \circ }$
  4. D $0 ^ { \circ } < \theta < 180 ^ { \circ }$
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Correct answer: D

11
Given that $| \overrightarrow { \mathrm { A } } | = | \overrightarrow { \mathrm { B } } |$. What is the angle between $( \bar { A } + \bar { B } )$ and $( \bar { A } - \bar { B } )$ ?
  1. A $30 ^ { \circ }$
  2. B $60 ^ { \circ }$
  3. C $90 ^ { \circ }$
  4. D $180 ^ { \circ }$
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Correct answer: C

12
A body is thrown horizontally from the top of a tower of 5 m height. It touches the ground at a distance of 10 m from the foot of the tower. The initial velocity of the body is; (g = 10 m/s$^{2}$)
  1. A $2.5 \mathrm{~ms}^{-1}$
  2. B $5.0 \mathrm{~ms}^{-1}$
  3. C $10 \mathrm{~ms}^{-1}$
  4. D $20 \mathrm{~ms}^{-1}$
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Correct answer: C

13
If the area of a triangle of sides $\overline { \mathrm { A } }$ & $\overline { \mathrm { B } }$ is equal to $\frac { \mathrm { AB } } { 4 }$, then find the angle between $\overline { \mathrm { A } }$ & $\overline { \mathrm { B } }$.
  1. A $30 ^ { \circ }$
  2. B $45 ^ { \circ }$
  3. C $60 ^ { \circ }$
  4. D $90 ^ { \circ }$
Show answer

Correct answer: A

14
A boat is rowed across a river (perpendicular to river flow) at the rate of 9 km/hr. The river flows at the rate of 12 km/hr. The velocity of the boat in km/hr is:
  1. A 14
  2. B 15
  3. C 16
  4. D 17
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Correct answer: B

15
A body moving along a circular path of radius R with velocity v, has centripetal acceleration a. If its velocity is made equal to 2v. What will be the centripetal acceleration?
  1. A 4a
  2. B 2a
  3. C $\frac { a } { 4 }$
  4. D $\frac { \mathrm { a } } { 2 }$
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Correct answer: A

16
The magnitude of the vector product of two vectors $\bar { A }$ and $\bar { B }$ may not be:
  1. A greater than AB
  2. B less than AB
  3. C equal to AB
  4. D equal to zero
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Correct answer: A

17
A man standing on a road holds his umbrella at $30 ^ { \circ }$ with the vertical to keep the rain away. He throws the umbrella and starts running at 10 km/h. He finds that raindrops are hitting his head vertically, the speed of raindrops with respect to the road will be;
  1. A 10 km/h
  2. B 20 km/h
  3. C 30 km/h
  4. D 40 km/h
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Correct answer: B

18
A ball is projected from a certain point on the surface of a planet at a certain angle with the horizontal surface. The horizontal and vertical displacement x and y varies with time t in second as: $\mathrm { x } = 10 \sqrt { 3 } \mathrm { t }$ and $\mathrm { y } = 10 \mathrm { t } - \mathrm { t } ^ { 2 }$. The maximum height attained by the ball is
  1. A 100 m
  2. B 75 m
  3. C 50 m
  4. D 25 m
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Correct answer: D

19
Rain is falling vertically with a speed of 3 m/s. If a man is running with the same speed then the velocity of rain w.r.t. man is:
  1. A 3 m/s
  2. B 6 m/s
  3. C 4.2 m/s
  4. D 0 m/s
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Correct answer: C

20
A stone is projected with velocity 80 m/s making an angle of 30° with the horizontal. The horizontal component of its velocity after 2 second is; (g = 10 m/s$^{2}$)
  1. A 40 m/s
  2. B 40√3 m/s
  3. C 20 m/s
  4. D 20√3 m/s
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Correct answer: B

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