Kinematics · JEE Main previous year questions

2021 18 questions

1. Q352021 · 1 Sept 2021 · Shift 2

   The ranges and heights for two projectiles projected with the same initial velocity at angles $42^{\circ }$ and $48^{\circ }$ with the horizontal are ${\mathrm{R}}_1$, ${\mathrm{R}}_2$ and ${\mathrm{H}}_1$, ${\mathrm{H}}_2$ respectively. Choose the correct option :

   1. A.${\mathrm{R}}_1>{\mathrm{R}}_2$ and ${\mathrm{H}}_1={\mathrm{H}}_2$
   2. B.${\mathrm{R}}_1={\mathrm{R}}_2$ and ${\mathrm{H}}_1<{\mathrm{H}}_2$
   3. C.${\mathrm{R}}_1<{\mathrm{R}}_2$ and ${\mathrm{H}}_1<{\mathrm{H}}_2$
   4. D.${\mathrm{R}}_1={\mathrm{R}}_2$ and ${\mathrm{H}}_1={\mathrm{H}}_2$
   Show answer

   Answer: B

2. Q332021 · 26 Aug 2021 · Shift 2

   A particle of mass m is suspended from a ceiling through a string of length L. The particle moves in a horizontal circle of radius r such that $r=\frac{L}{\sqrt{2}}$. The speed of particle will be :

   1. A.$\sqrt{rg}$
   2. B.$\sqrt{2rg}$
   3. C.$2\sqrt{rg}$
   4. D.$\sqrt{\frac{rg}{2}}$
   Show answer

   Answer: A

3. Q552021 · 27 Jul 2021 · Shift 2· Numerical answer
   
   Show answer

   Answer: 30

4. Q512021 · 25 Jul 2021 · Shift 1· Numerical answer

   A body of mass 2 kg moving with a speed of 4 m/s makes an elastic collision with another body at rest and continues to move in the original direction but with one fourth of its initial speed. The speed of the two body centre of mass is $\frac{x}{10}$ m/s. Then the value of x is ____.

   Show answer

   Answer: 25

5. Q332021 · 25 Jul 2021 · Shift 2

   A force $\vec{F}=(40\hat{i}+10\hat{j})N$ acts on a body of mass 5 kg. If the body starts from rest, its position vector $\vec{r}$ at time t = 10 s, will be :

   1. A.$(100\hat{i}+400\hat{j})m$
   2. B.$(100\hat{i}+100\hat{j})m$
   3. C.$(400\hat{i}+100\hat{j})m$
   4. D.$(400\hat{i}+400\hat{j})m$
   Show answer

   Answer: C

6. Q472021 · 22 Jul 2021 · Shift 2
   
   1. A.$C=\sqrt{\frac{2v(0{)}^2}{{\omega }^2}+x(0{)}^2},\varphi ={\tan }^{-1}\left(\frac{x(0)\omega }{2v(0)}\right)$
   2. B.$C=\sqrt{\frac{v(0{)}^2}{{\omega }^2}+x(0{)}^2},\varphi ={\tan }^{-1}\left(\frac{x(0)\omega }{v(0)}\right)$
   3. C.$C=\sqrt{\frac{v(0{)}^2}{{\omega }^2}+x(0{)}^2},\varphi ={\tan }^{-1}\left(\frac{v(0)}{x(0)\omega }\right)$
   4. D.$C=\sqrt{\frac{2v(0{)}^2}{{\omega }^2}+x(0{)}^2},\varphi ={\tan }^{-1}\left(\frac{v(0)}{x(0)\omega }\right)$
   Show answer

   Answer: C

7. Q372021 · 20 Jul 2021 · Shift 1

   A butterfly is flying with a velocity $4\sqrt{2}\text{ m/s}$ in North-East direction. Wind is slowly blowing at $1\text{ m/s}$ from North to South. The resultant displacement of the butterfly in 3 seconds is :

   1. A.$12\sqrt{2}\text{ m}$
   2. B.$20\text{ m}$
   3. C.$3\text{ m}$
   4. D.$15\text{ m}$
   Show answer

   Answer: D

8. Q552021 · 18 Mar 2021 · Shift 1· Numerical answer

   A person is swimming with a speed of 10 m/s at an angle of $120^{\circ }$ with the flow and reaches to a point directly opposite on the other side of the river. The speed of the flow is 'x' m/s. The value of 'x' to the nearest integer is _______.

   Show answer

   Answer: 5

9. Q572021 · 18 Mar 2021 · Shift 1· Numerical answer
   
   Show answer

   Answer: 20

10. Q392021 · 18 Mar 2021 · Shift 2
    
    1. A.
    2. B.
    3. C.
    4. D.
    Show answer

    Answer: A

11. Q542021 · 18 Mar 2021 · Shift 2· Numerical answer

    A ball of mass $4\mathrm{kg}$, moving with a velocity of $10\mathrm{m}{\mathrm{s}}^{-1}$, collides with a spring of length $8\mathrm{m}$ and force constant $100\mathrm{N}{\mathrm{m}}^{-1}$. The length of the compressed spring is x m. The value of x, to the nearest integer, is ____.

    Show answer

    Answer: 6

12. Q322021 · 16 Mar 2021 · Shift 1
    
    1. A.
    2. B.
    3. C.
    4. D.
    Show answer

    Answer: A

13. Q582021 · 16 Mar 2021 · Shift 1· Numerical answer
    
    Show answer

    Answer: 30

14. Q552021 · 26 Feb 2021 · Shift 1· Numerical answer

    A boy pushes a box of mass 2 kg with a force $\vec{F}=\left(20\hat{i}+10\hat{j}\right)\mathrm{N}$ on a frictionless surface. If the box was initially at rest, then _________ m is displacement along the x-axis after 10s.

    Show answer

    Answer: 500

15. Q422021 · 26 Feb 2021 · Shift 2

    The trajectory of a projectile in a vertical plane is $y=\alpha x-\beta x^2$, where $\alpha$ and $\beta$ are constants and x & y are respectively the horizontal and vertical distances of the projectile from the point of projection. The angle of projection $\theta$ and the maximum height attained H are respectively given by :

    1. A.${\tan }^{-1}\alpha ,\frac{{\alpha }^2}{4\beta }$
    2. B.${\tan }^{-1}\alpha ,\frac{4{\alpha }^2}{\beta }$
    3. C.${\tan }^{-1}\left(\frac{\beta }{\alpha }\right),\frac{{\alpha }^2}{\beta }$
    4. D.${\tan }^{-1}\beta ,\frac{{\alpha }^2}{2\beta }$
    Show answer

    Answer: A

16. Q472021 · 26 Feb 2021 · Shift 2

    A particle executes S.H.M., the graph of velocity as a function of displacement is :

    1. A.a parabola
    2. B.a helix
    3. C.an ellipse
    4. D.a circle
    Show answer

    Answer: C

17. Q522021 · 26 Feb 2021 · Shift 2· Numerical answer

    A particle executes S.H.M. with amplitude 'a', and time period 'T'. The displacement of the particle when its speed is half of maximum speed is $\frac{\sqrt{x}a}{2}$. The value of x is _________.

    Show answer

    Answer: 3

18. Q422021 · 25 Feb 2021 · Shift 2

    $Y=A\sin (\omega t+{\varphi }_0)$ is the time-displacement equation of a SHM. At $t=0$ the displacement of the particle is $Y=\frac{A}{2}$ and it is moving along negative x-direction. Then the initial phase angle ${\varphi }_0$ will be:

    1. A.$\frac{5\pi }{6}$
    2. B.$\frac{\pi }{3}$
    3. C.$\frac{2\pi }{3}$
    4. D.$\frac{\pi }{6}$
    Show answer

    Answer: A